[Indigo]<3DGraphics>NewThreeDRender>PatchFromPolyProcs.mesa!2

PatchFromPolyProcs.mesa

Last Edited by: Crow, March 16, 1988 6:16:21 pm PST

Bloomenthal, September 14, 1988 1:06:44 pm PDT

DIRECTORY

Atom USING [ DottedPair, DottedPairNode, GetPropFromList, PropList,
PutPropOnList, RemPropFromList ],

Basics USING [ BITOR, BITAND ],

RealFns USING [ AlmostEqual, SqRt ],

G3dVector USING [ Add, Cross, Div, Dot, Length, Mul,
NearestToLine, Negate, Normalize, Sub ],

G3dMatrix USING [ Mul, TransformVec ],

G3dBasic USING [ Ray ],

G3dSpline USING [ Coeffs, Position, CoeffsFromBezier, CoeffsFromHermite ],

ScanConvert USING [ justNoticeable ],

MappedAndSolidTexture USING [ AdjustTexture ],

ThreeDBasics USING [ AllOut, ClipState, Context, Error, FacingDir,
GetSurfaceType, NatSequence, NoneOut, OutCode, Patch,
PatchProc, PatchSequence, Pair, PtrPatch, PtrPatchSequence,
RealSequence, RegisterSurfaceType, RGB,
ShadingSequence, ShadingValue, ShapeClass, ShapeInstance,
ShapeProc, SixSides, Triple, TripleSequence, Vertex, VertexInfo,
VertexInfoProc, VertexInfoSequence, VertexSequence, Xfm3D ],

ShapeUtilities USING [ GetClipCodeForPt, GetPatch, GetPatchClipState,
GetVtxNmls, GetVtxShades, ReleasePatch, ShadePoly,
XfmPtToDisplay, XfmPtToEyeSpace, XfmToEyeSpace
],

SurfaceRender USING [ GetPtrPatchClipState, OutputPolygon, ValidatePolyhedron ];

PatchFromPolyProcs: CEDAR MONITOR

IMPORTS Atom, Basics, G3dMatrix, G3dSpline, G3dVector, MappedAndSolidTexture, RealFns, ShapeUtilities, SurfaceRender, ThreeDBasics

= BEGIN

Types

Ray: TYPE ~ G3dBasic.Ray;

NatSequence: TYPE ~ ThreeDBasics.NatSequence;

Pair: TYPE ~ ThreeDBasics.Pair;

Triple: TYPE ~ ThreeDBasics.Triple;

TripleSequence: TYPE ~ ThreeDBasics.TripleSequence;

RGB: TYPE ~ ThreeDBasics.RGB;

RealSequence: TYPE ~ ThreeDBasics.RealSequence;

Context: TYPE ~ ThreeDBasics.Context;

SixSides: TYPE ~ ThreeDBasics.SixSides;

Xfm3D: TYPE ~ ThreeDBasics.Xfm3D;

ShapeInstance: TYPE ~ ThreeDBasics.ShapeInstance;

Patch: TYPE ~ ThreeDBasics.Patch;

PatchSequence: TYPE ~ ThreeDBasics.PatchSequence;

PatchProc: TYPE ~ ThreeDBasics.PatchProc;

PtrPatch: TYPE ~ ThreeDBasics.PtrPatch;

PtrPatchSequence: TYPE ~ ThreeDBasics.PtrPatchSequence;

Vertex: TYPE ~ ThreeDBasics.Vertex;

VertexInfo: TYPE ~ ThreeDBasics.VertexInfo;

RECORD[coord: Vertex, shade: ShadingValue, props: Atom.PropList, aux: REF ANY];

VertexInfoSequence: TYPE ~ ThreeDBasics.VertexInfoSequence;

VertexInfoProc: TYPE ~ ThreeDBasics.VertexInfoProc;

ShadingValue: TYPE ~ ThreeDBasics.ShadingValue;

ShapeClass: TYPE ~ ThreeDBasics.ShapeClass;

ShapeProc: TYPE ~ ThreeDBasics.ShapeProc;

ClipState: TYPE ~ ThreeDBasics.ClipState;

OutCode: TYPE ~ ThreeDBasics.OutCode;

AllOut: OutCode ~ ThreeDBasics.AllOut;

NoneOut: OutCode ~ ThreeDBasics.NoneOut;

FacingDir: TYPE ~ ThreeDBasics.FacingDir;

LORA: TYPE = LIST OF REF ANY;

MidPtProc: TYPE ~ PROC[v0, v1: REF VertexInfo] RETURNS[REF VertexInfo];

nullTriple: Triple ~ [0.0, 0.0, 0.0];

Corner: TYPE ~ RECORD [ inVtx, outVtx: NAT ← 0,
inDir, outDir, normal, interiorKnot: Triple ← nullTriple,
concave: BOOLEAN ← FALSE ];

Represents a corner of a polygon,
- inVtx is the vertex at the other end of the incoming edge (previous vertex in order),
- outVtx is other vertex on outgoing edge,
- inDir, outDir are the corresponding outward direction vectors,
- normal is the carefully determined normal vector
- concave = TRUE indicates corner is concave vertex needing reversed cross product.

CornerSeq: TYPE ~ RECORD [ length: NAT ← 0, s: SEQUENCE maxLength: NAT OF Corner ];

CornerSeqSeq: TYPE ~ RECORD [ length: NAT ← 0,
s: SEQUENCE maxLength: NAT OF REF CornerSeq ];

TangentSet: TYPE ~ RECORD [t0, et0, t1, et1: Triple ← nullTriple];

Represents the tangents at the endpoints of an edge (in object space and eyespace), the edge is ordered in the vertex order of the polygon (t0 at leading endpoint, t1 at trailing endpoint)

TangentSeq: TYPE ~ RECORD [length: NAT ← 0, s: SEQUENCE maxLength: NAT OF TangentSet];

TangentTriple: TYPE ~ ARRAY [0..3) OF TangentSet;

TangentQuad: TYPE ~ ARRAY [0..4) OF TangentSet;

TangentSeqSeq: TYPE ~ RECORD [

length: NAT ← 0, s: SEQUENCE maxLength: NAT OF REF TangentSeq];

Triangle: TYPE ~ RECORD [ v: ARRAY[0..3) OF VertexInfo, t: ARRAY[0..3) OF TangentSet ];

NatSequenceSequence: TYPE ~ RECORD [
length: NAT ← 0, s: SEQUENCE maxLength: NAT OF REF NatSequence ];

BoolSequence: TYPE ~ RECORD [length: NAT ← 0, s: SEQUENCE maxLength: NAT OF BOOLEAN];

Renamed Procedures

Add: PROC[v1, v2: Triple] RETURNS[Triple] ~ G3dVector.Add;

Mul: PROC[v: Triple, s: REAL] RETURNS[Triple] ~ G3dVector.Mul;

Cross: PROC[v1, v2: Triple] RETURNS[Triple] ~ G3dVector.Cross;

Div: PROC[v: Triple, s: REAL] RETURNS[Triple] ~ G3dVector.Div;

Dot: PROC[v1, v2: Triple] RETURNS[REAL] ~ G3dVector.Dot;

Length: PROC[v: Triple] RETURNS[REAL] ~ G3dVector.Length;

Negate: PROC[v: Triple] RETURNS[Triple] ~ G3dVector.Negate;

Nmlize: PROC[v: Triple] RETURNS[Triple] ~ G3dVector.Normalize;

Sub3: PROC[v1, v2: Triple] RETURNS[Triple] ~ G3dVector.Sub;

GetProp: PROC [propList: Atom.PropList, prop: REF ANY] RETURNS [REF ANY] ~
Atom.GetPropFromList;

PutProp: PROC [propList: Atom.PropList, prop: REF ANY, val: REF ANY]
RETURNS [Atom.PropList] ~ Atom.PutPropOnList;

Global Variables

maxDeviation: REAL ← .5; -- subdivision tolerance with antialiasing

maxJaggyDeviation: REAL ← 2.0; -- jaggy subdivision tolerance (pixels)

closenessFactor: REAL ← 10.0; -- times maxDeviation gets clipping cutoff for straightness

recurseLimit: NAT ← 14; -- safety valve on recursion

minCosToAlign: REAL ← -0.866; -- Align edges if they meet at > 150 degrees

minCosToAlignOpen: REAL ← 0.707; -- Align open edges if they meet at > 45 degrees

stopIfStraight: BOOLEAN ← TRUE; -- set false to defeat termination algorithm

unitizeNormals: BOOLEAN ← FALSE; -- treat all polygons equally when making vertex normal

showLines: BOOLEAN; -- debug and pedagogical aid

Utility Procedures

PutPropSafely: PROC[propList: Atom.PropList, prop, val: REF ANY] RETURNS[Atom.PropList] ~{

Put property on new property list, to avoid clobbering other lists inherited from same place

newProps: Atom.PropList ← NIL;

FOR list: Atom.PropList ← propList, list.rest UNTIL list = NIL DO -- new proplist

element: Atom.DottedPair ← NEW[Atom.DottedPairNode ← list.first^];

newProps ← CONS[element, newProps];

ENDLOOP;

RETURN[ PutProp[ newProps, prop, val ] ];

};

RemPropSafely: PROC[ propList: Atom.PropList, prop: REF ANY ] RETURNS[Atom.PropList] ~ {

Remove property from new property list, to avoid clobbering lists inherited from same place

newProps: Atom.PropList ← NIL;

FOR list: Atom.PropList ← propList, list.rest UNTIL list = NIL DO -- new proplist

element: Atom.DottedPair ← NEW[Atom.DottedPairNode ← list.first^];

newProps ← CONS[element, newProps];

ENDLOOP;

RETURN[ Atom.RemPropFromList[ newProps, prop ] ];

};

Sqr: PROCEDURE [number: REAL] RETURNS [REAL] ~ INLINE { RETURN[number * number]; };

Sub: PROC[f, g: REAL] RETURNS[REAL] ~ {

Difference f - g, returns zero if less than 3 decimal places

IF RealFns.AlmostEqual[f, g, -10] THEN RETURN [0.0] ELSE RETURN[f-g];

};

Sub1: PROC[f, g: REAL] RETURNS[REAL] ~ {

Screen space f - g, returns zero if less than noticeable

result: REAL ← f-g;

IF ABS[result] < ScanConvert.justNoticeable THEN RETURN [0.0] ELSE RETURN[result];

};

DiffPosns: PROC[vtx1, vtx2: Vertex, space: ATOM ← NIL] RETURNS[Triple] ~ {

Subtracts vtx2 from vtx1 in selected space

SELECT space FROM

$Eye => RETURN[[Sub[vtx1.ex, vtx2.ex], Sub[vtx1.ey, vtx2.ey], Sub[vtx1.ez, vtx2.ez]]];

$Screen=> RETURN[[Sub1[vtx1.sx, vtx2.sx], Sub1[vtx1.sy, vtx2.sy], Sub1[vtx1.sz, vtx2.sz]]];

ENDCASE => -- object space

RETURN[[Sub[vtx1.x, vtx2.x], Sub[vtx1.y, vtx2.y], Sub[vtx1.z, vtx2.z]]];

};

GetSlopeVec: PROC[normal, edge: Triple, hermite: BOOL ← FALSE] RETURNS[slope: Triple] ~ {

Returns a vector normal to the 1st vector and in the plane defined by both vectors

Magnitude is scaled to equal that of second vector ("edge")

Magnitude is scaled to to proper length for Bezier inner control pt approximating circular arc

slope ← Cross[ Cross[normal, edge], normal ];

IF hermite

THEN slope ← G3dVector.Mul[ Nmlize[slope], Length[edge] ]

THEN slope ← G3dVector.Mul[ ScaleTangent[ slope, edge ], 3.0 ]

ELSE slope ← ScaleTangent[ slope, edge ];

};

GetNmlVec: PROC[vec: Triple, p: VertexInfo, reverse: BOOL ← FALSE]
RETURNS[nmlVec: Triple] ~ {

Returns a normalized vector normal to the 1st vector and in the plane defined by 2nd

normal: Triple ← [p.shade.exn, p.shade.eyn, p.shade.ezn];

nmlVec ← IF reverse

THEN Nmlize[ Cross[normal, vec] ]

ELSE Nmlize[ Cross[vec, normal] ];

};

ScaleTangent: PROC[tangent, edgeDir: Triple] RETURNS[Triple] ~ {

Scale tangent vector to proper length for Bezier inner control pt approximating circular arc

adjSide, oppSide, scale: REAL;

edgeLength: REAL ← Length[edgeDir];

hypotenuse: REAL ← Length[tangent];

IF edgeLength = 0.0 OR hypotenuse = 0.0 THEN RETURN [[0.0, 0.0, 0.0]];

adjSide ← ABS[Dot[edgeDir, tangent] / edgeLength];

oppSide ← IF adjSide >= hypotenuse

THEN 0.0

ELSE RealFns.SqRt[hypotenuse*hypotenuse - adjSide*adjSide];

scale ← IF oppSide/hypotenuse > .01

THEN edgeLength * 2.0 * (hypotenuse - adjSide) / (3.0 * oppSide * oppSide)

ELSE .333333 * edgeLength / hypotenuse;

RETURN[ G3dVector.Mul[ tangent, scale ] ];

};

TooClose: PROC[ context: REF Context, v: Vertex, outCode: OutCode, tol: REAL ]
RETURNS[BOOLEAN] ~ {

Find max distance from screen edge on inside

maxDist: REAL ← 0.0;

IF v.sz = 0.0 THEN RETURN [FALSE]; -- invalid screen coord, ignore

IF outCode.left

THEN maxDist ← MAX[maxDist, v.sx - context.viewPort.x];

IF outCode.right

THEN maxDist ← MAX[maxDist, context.viewPort.w + context.viewPort.x - v.sx];

IF outCode.bottom

THEN maxDist ← MAX[maxDist, v.sy - context.viewPort.y];

IF outCode.top

THEN maxDist ← MAX[maxDist, context.viewPort.h + context.viewPort.y - v.sy];

IF maxDist < tol * closenessFactor THEN RETURN[TRUE] ELSE RETURN[FALSE];

};

EdgeStraight: PROC[context: REF Context, v0, v1: VertexInfo, slope1, slope2: Triple, tol: REAL]
RETURNS[BOOL] ~ {

Tests for slopes within n pixels of edge on screen

pos1: Triple ← ShapeUtilities.XfmPtToDisplay[ context, -- near slope plus near end

Add[[v0.coord.ex, v0.coord.ey, v0.coord.ez], slope1 ]

];

pos2: Triple ← ShapeUtilities.XfmPtToDisplay[ context, -- far slope plus near end

Add[[v0.coord.ex, v0.coord.ey, v0.coord.ez], slope2 ]

];

distance: REAL ← ABS[pos1.x - v1.coord.sx] + ABS[pos1.y - v1.coord.sy]
+ ABS[pos2.x - v1.coord.sx] + ABS[pos2.y - v1.coord.sy];

distance ← distance / 4.0; -- summed manhattan distances / 4 estimates deviation

distance ← distance / 2.0; -- heuristic (fudge factor)

IF distance <= tol THEN RETURN[TRUE] ELSE RETURN[FALSE];

};

PatchDepthSort: PROC[context: REF Context, p: REF PatchSequence]
RETURNS[REF PatchSequence] ~ {

z: REF RealSequence ← NEW[RealSequence[p.length]];

pOut: REF PatchSequence ← NEW [PatchSequence[p.length]];

FOR i: NAT IN [0..p.length) DO -- Get average of depths at vertices

z[i] ← 0.0;

FOR j: NAT IN [0..p[i].nVtces) DO z[i] ← z[i] + p[i][j].coord.ez; ENDLOOP;

z[i] ← z[i] / p[i].nVtces;

pOut[i] ← p[i];

ENDLOOP;

FOR i: NAT IN [1..p.length) DO

FOR j: NAT DECREASING IN [0..i) DO -- bubble sort to increasing depth order

IF z[j+1] < z[j] THEN {

t: REAL ← z[j+1]; p: REF Patch ← pOut[j+1];

z[j+1] ← z[j]; pOut[j+1] ← pOut[j];

z[j] ← t; pOut[j] ← p;

};

ENDLOOP;

IF NOT context.antiAliasing THEN FOR i: NAT IN [0..p.length/2) DO -- re-order back-to-front

j: NAT ← p.length-1 - i;

tmpP: REF Patch ← pOut[i]; pOut[i] ← pOut[j]; pOut[j] ← tmpP;

ENDLOOP;

pOut.length ← p.length;

RETURN[pOut];

};

ValidatePatchPoly: ShapeProc ~ {

PROC[context: REF Context, shape: REF ShapeInstance, data: REF] RETURNS[REF ShapeInstance];

doAlways: BOOLEAN ← IF data # NIL THEN TRUE ELSE FALSE;

IF GetProp[shape.shadingProps, $VtxInfoComputed] = NIL

THEN ShapeUtilities.GetVtxNmls[context, shape]; -- calculate normals if not read in

Update shading and transform matrices

IF shape.vtcesInValid THEN {

xfm: Xfm3D ← G3dMatrix.Mul[shape.position, context.eyeSpaceXfm];

Transform vertices to eyespace, get clip state of vertices and whole shape

shape.clipState ← ShapeUtilities.XfmToEyeSpace[ context, shape ];

Transform normals to eyespace

IF shape.clipState # out THEN FOR i: NAT IN [0..shape.shade.length) DO

OPEN shape.shade[i]; -- transform normal vectors

[ [exn, eyn, ezn] ] ← G3dMatrix.TransformVec[ [xn, yn, zn] , xfm];

ENDLOOP;

IF shape.surface # NIL THEN { -- get clipping info for patches

patch: REF PtrPatchSequence ← NARROW[shape.surface];

FOR i: NAT IN [0..shape.numSurfaces) DO

IF patch[i] # NIL

THEN IF shape.clipState = in

THEN patch[i].clipState ← in -- unclipped, inside

ELSE IF shape.clipState = clipped -- evaluate clipping tags

THEN SurfaceRender.GetPtrPatchClipState[ shape, patch[i] ]

ELSE patch[i].clipState ← out;

ENDLOOP;

};

shape.vtcesInValid ← FALSE;

};

IF shape.shadingInValid AND (shape.clipState # out OR doAlways)

THEN ShapeUtilities.GetVtxShades[ context, shape ];

shape.shadingInValid ← FALSE;

RETURN[shape];

};

Display Procedures

DisplayNothing: PatchProc ~ { -- dummy routine for timing tests

shape: REF ShapeInstance ← NARROW[ GetProp[patch.props, $Shape] ];

IF patch # NIL THEN ShapeUtilities.ReleasePatch[patch]; -- end of life for patch

RETURN[ NIL ];

};

DisplayPatchEdges: PatchProc ~ {

PROC[ context: REF Context, patch: REF Patch, data: REF ANY ← NIL ] RETURNS[REF Patch]

shape: REF ShapeInstance ← NARROW[ GetProp[patch.props, $Shape] ];

patchNo: NAT ← NARROW[ GetProp[patch.props, $PatchNo], REF NAT ]^;

tangents: REF TangentSeqSeq ← NARROW[ GetProp[shape.fixedProps, $PatchTangents] ];

corners: REF CornerSeqSeq ← NARROW[ GetProp[shape.fixedProps, $PatchCorners] ];

xfm: Xfm3D ← G3dMatrix.Mul[shape.position, context.eyeSpaceXfm];

clr: RGB ← shape.shadingClass.color;

npts: NAT ← IF data # NIL THEN NARROW[data, REF NAT]^ ELSE 8;

FOR i: NAT IN [0..patch.nVtces) DO

j: NAT ← (i+1) MOD patch.nVtces;

outP: REF Patch ← ShapeUtilities.GetPatch[npts];

outState: OutCode ← AllOut; inState: OutCode ← NoneOut;

coeffs: G3dSpline.Coeffs;

SELECT patch.type FROM

$PolygonWithNormals => coeffs ← GetEdgeCurveNmls[ patch[i], patch[j] ];

$PolygonWithTangents, $PolygonToTnsrPatch => coeffs ← GetEdgeCurveTngs[

patch[i], patch[j], tangents[patchNo][i]

];

ENDCASE => SIGNAL ThreeDBasics.Error[[$Unimplemented, "Unknown surface type"]];

FOR k: NAT IN [0..npts) DO

OPEN outP[k].coord;

t: REAL ← 1.0 * k / (npts-1);

[[x, y, z]] ← G3dSpline.Position[coeffs, t];

[[ex, ey, ez], clip] ← ShapeUtilities.XfmPtToEyeSpace[context, [x, y, z], xfm];

clip ← ShapeUtilities.GetClipCodeForPt[ context, [ex, ey, ez] ];

IF clip = NoneOut

THEN [[sx, sy, sz]] ← ShapeUtilities.XfmPtToDisplay[context, [ex, ey, ez]];

outState ← LOOPHOLE[ Basics.BITAND[LOOPHOLE[outState], LOOPHOLE[clip]] ];

inState ← LOOPHOLE[ Basics.BITOR[LOOPHOLE[inState], LOOPHOLE[clip]] ];

[outP[k].shade.er, outP[k].shade.eg, outP[k].shade.eb] ← clr; -- use shape color

ENDLOOP;

outP.type ← $PolyLine;

outP.props ← patch.props;

outP.nVtces ← npts;

outP.clipState ← IF inState = NoneOut

THEN in

ELSE IF outState # NoneOut THEN out ELSE clipped;

[outP] ← SurfaceRender.OutputPolygon[context, outP];

ENDLOOP;

RETURN[NIL];

};

Initialization of Classes

InitClasses: PROC[] ~ { -- register procedures for basic surface types

standardClass: ShapeClass ← ThreeDBasics.GetSurfaceType[$ConvexPolygon];

standardClass.type ← $PolygonWithNormals;

standardClass.validate ← ValidatePatchPoly;

standardClass.displayPatch ← DisplayPatchNmls;

ThreeDBasics.RegisterSurfaceType[standardClass, $PolygonWithNormals];

standardClass.type ← $PolygonWithTangents;

standardClass.validate ← ValidatePolyWTangents;

standardClass.displayPatch ← DisplayPatchTngs;

ThreeDBasics.RegisterSurfaceType[standardClass, $PolygonWithTangents];

standardClass.type ← $PolygonToTnsrPatch;

standardClass.displayPatch ← DisplayPatchTnsr;

ThreeDBasics.RegisterSurfaceType[standardClass, $PolygonToTnsrPatch];

standardClass.type ← $PolygonNoImage;

standardClass.validate ← SurfaceRender.ValidatePolyhedron;

standardClass.displayPatch ← DisplayNothing;

ThreeDBasics.RegisterSurfaceType[standardClass, $PolygonNoImage];

};

Utilities for expansion of non-planar polygons

TriangulateAndDisplay: PatchProc ~ {

Subdivide polygon to triangular patches, depth sort, then call TriangleDisplay on each one

tol: REAL ← IF context.antiAliasing THEN maxDeviation ELSE maxJaggyDeviation;

tangents: REF TangentSeq ← NARROW[ data ];

IF patch.nVtces < 3 THEN SIGNAL ThreeDBasics.Error[[$MisMatch, "Not enough vertices"]];

IF patch.nVtces = 3

THEN {

IF patch.type = $PolygonWithTangents THEN patch.props ← PutPropSafely[

patch.props, $Tangents,

NEW[TangentTriple ← [

NmlizeTangentSet[ patch[0], patch[1], tangents[0] ],

NmlizeTangentSet[ patch[1], patch[2], tangents[1] ],

NmlizeTangentSet[ patch[2], patch[0], tangents[2] ]

]]

];

TriangleDisplay[context, patch, 0, tol];

patch ← NIL; -- nil out patch so it won't be returned by caller

}

ELSE {

outPatch: REF PatchSequence ← NEW [PatchSequence[patch.nVtces]];

midPt: VertexInfo ← GetCenterPt[context, patch, tangents];

midTangents: REF TangentSeq ← NARROW[

GetProp[midPt.props, $Tangents]

];

FOR i: NAT IN [0..patch.nVtces) DO

j: NAT ← (i + 1) MOD patch.nVtces; -- next vertex

outPatch[i] ← ShapeUtilities.GetPatch[3]; -- released by display action

outPatch[i].type ← patch.type;

outPatch[i].oneSided ← patch.oneSided;

outPatch[i].nVtces ← 3;

outPatch[i].clipState ← patch.clipState;

outPatch[i].dir ← undetermined;

outPatch[i].props ← patch.props;

outPatch[i][0] ← patch[i];

outPatch[i][1] ← patch[(i+1) MOD patch.nVtces];

outPatch[i][2] ← midPt;

IF patch.type = $PolygonWithTangents THEN outPatch[i].props ← PutPropSafely[

outPatch[i].props, $Tangents,

NEW[TangentTriple ← [

NmlizeTangentSet[ outPatch[i][0], outPatch[i][1], tangents[i] ], -- orig. edge

midTangents[j], -- in to middle, from next vertex

[ t0: midTangents[i].t1, et0: midTangents[i].et1, -- back out to current vertex
t1: midTangents[i].t0, et1: midTangents[i].et0 ]

]]

];

IF outPatch[i].clipState # in THEN ShapeUtilities.GetPatchClipState[ outPatch[i] ];

ENDLOOP;

outPatch.length ← patch.nVtces;

outPatch ← PatchDepthSort[ context, outPatch ]; -- sort to depth order

FOR i: NAT IN [0..patch.nVtces) DO

TriangleDisplay[context, outPatch[i], 0, tol];

ENDLOOP;

};

RETURN[patch];

};

GetCenterPt: PROC[context: REF Context, patch: REF Patch, tangents: REF TangentSeq ← NIL]
RETURNS[midPt: VertexInfo] ~ {

Find central point in polygon for use in triangulation

shape: REF ShapeInstance ← NARROW[ GetProp[patch.props, $Shape] ];

tol: REAL ← IF context.antiAliasing THEN maxDeviation ELSE maxJaggyDeviation;

IF patch.nVtces <= 3 THEN SIGNAL ThreeDBasics.Error[[$MisMatch, "Not enough vertices"]];

{

midTangents: REF TangentSeq ← IF patch.type = $PolygonWithTangents
OR patch.type = $PolygonToTnsrPatch

THEN NEW[ TangentSeq[patch.nVtces] ] ELSE NIL;

lerpProc: VertexInfoProc ← IF shape # NIL THEN shape.shadingClass.lerpVtxAux ELSE NIL;

halfVtces: NAT ← patch.nVtces / 2;

loopEnd: NAT ← IF halfVtces * 2 # patch.nVtces THEN patch.nVtces
ELSE patch.nVtces/2;

midPt.shade.r ← midPt.shade.g ← midPt.shade.b ← midPt.shade.t ← 0.0;

FOR i: NAT IN [0..loopEnd) DO -- guess at middle point, (odd # of Vtces will be too flat)

pt: VertexInfo; flat: BOOLEAN; -- sum vertices given by each opposing vertex pair

t, t0, t1: TangentSet;

j: NAT ← (i + halfVtces) MOD patch.nVtces; -- vertex across poly from this one

IF patch.type = $PolygonWithTangents OR patch.type = $PolygonToTnsrPatch

THEN { -- get sum of outgoing and incoming tangents at vertex for midpt direction

offst0, offst1: Triple;

k: NAT ← (i + patch.nVtces-1) MOD patch.nVtces; -- previous vertex in polygon

offst0 ← tangents[i].et0;

t.et0 ← Add[ tangents[i].et0, tangents[k].et1 ];

k ← (j + patch.nVtces-1) MOD patch.nVtces; -- previous vertex across polygon

offst1 ← tangents[k].et1;

t.et1 ← Add[ tangents[j].et0, tangents[k].et1 ];

t ← NmlizeTangentSet[ patch[i], patch[j], t ];

[pt, t0, t1, flat] ← CurveDivideTan[

context, patch[i], patch[j], t.et0, t.et1, offst0, offst1, 0.5, tol];

In following, t0 toward center at vertex, t1 away from center at center

midTangents[i] ← t0;

midTangents[j] ← [t0: t1.t1, et0: t1.et1, t1: t1.t0, et1: t1.et0 ]; -- reverse order

}

ELSE {

[pt, flat] ← TriangleCurveDivideNml[context, patch[i], patch[j], 0, tol];

midPt.shade.exn ← midPt.shade.exn + pt.shade.exn;

midPt.shade.eyn ← midPt.shade.eyn + pt.shade.eyn;

midPt.shade.ezn ← midPt.shade.ezn + pt.shade.ezn;

};

midPt.coord.ex ← midPt.coord.ex + pt.coord.ex;

midPt.coord.ey ← midPt.coord.ey + pt.coord.ey;

midPt.coord.ez ← midPt.coord.ez + pt.coord.ez;

midPt.shade.r ← midPt.shade.r + pt.shade.r;

midPt.shade.g ← midPt.shade.g + pt.shade.g;

midPt.shade.b ← midPt.shade.b + pt.shade.b;

midPt.shade.t ← midPt.shade.t + pt.shade.t;

IF shape.shadingClass.texture # NIL THEN { -- for textures

midPt.coord.x ← midPt.coord.x + pt.coord.x;

midPt.coord.y ← midPt.coord.y + pt.coord.y;

midPt.coord.z ← midPt.coord.z + pt.coord.z;

midPt.shade.xn ← midPt.shade.xn + pt.shade.xn;

midPt.shade.yn ← midPt.shade.yn + pt.shade.yn;

midPt.shade.zn ← midPt.shade.zn + pt.shade.zn;

IF lerpProc # NIL AND pt.aux # NIL THEN IF i = 0 -- get aux. info from class proc

THEN midPt ← shape.shadingClass.loadVtxAux[ NIL, midPt, pt.aux]

ELSE {

data: LORA ← LIST[ midPt.aux, pt.aux, NEW[REAL ← 1.0], NEW[REAL ← 1.0] ];

midPt ← lerpProc[ NIL, midPt, data];

};

ENDLOOP;

midPt.coord.ex ← midPt.coord.ex / loopEnd; -- get average by dividing by no. edges

midPt.coord.ey ← midPt.coord.ey / loopEnd;

midPt.coord.ez ← midPt.coord.ez / loopEnd;

IF patch.type = $PolygonWithTangents OR patch.type = $PolygonToTnsrPatch

THEN { -- get mid-normal by cross-products on mid-tangents

FOR i: NAT IN [0..loopEnd-1) DO

[[midPt.shade.exn, midPt.shade.eyn, midPt.shade.ezn]] ← Add[

[midPt.shade.exn, midPt.shade.eyn, midPt.shade.ezn],

Cross[midTangents[i].et1, midTangents[i+1].et1]

];

ENDLOOP;

[[midPt.shade.exn, midPt.shade.eyn, midPt.shade.ezn]] ← Nmlize[

[midPt.shade.exn, midPt.shade.eyn, midPt.shade.ezn]

];

FOR i: NAT IN [0..patch.nVtces) DO -- Rebuild midtangents using middle point

midTangents[i].et0 ← GetSlopeVec[

[patch[i].shade.exn, patch[i].shade.eyn, patch[i].shade.ezn],

DiffPosns[midPt.coord, patch[i].coord, $Eye]

];

midTangents[i].et1 ← GetSlopeVec[

[midPt.shade.exn, midPt.shade.eyn, midPt.shade.ezn],

DiffPosns[patch[i].coord, midPt.coord, $Eye]

];

ENDLOOP;

}

ELSE {

midPt.shade.exn ← midPt.shade.exn / loopEnd;

midPt.shade.eyn ← midPt.shade.eyn / loopEnd;

midPt.shade.ezn ← midPt.shade.ezn / loopEnd;

};

midPt.shade.r ← midPt.shade.r / loopEnd;

midPt.shade.g ← midPt.shade.g / loopEnd;

midPt.shade.b ← midPt.shade.b / loopEnd;

midPt.shade.t ← midPt.shade.t / loopEnd;

IF shape.shadingClass.texture # NIL THEN { -- for solid textures

midPt.coord.x ← midPt.coord.x / loopEnd;

midPt.coord.y ← midPt.coord.y / loopEnd;

midPt.coord.z ← midPt.coord.z / loopEnd;

IF patch.type = $PolygonWithTangents OR patch.type = $PolygonToTnsrPatch

THEN { -- get mid-normal by cross-products on mid-tangents

FOR i: NAT IN [0..loopEnd-1) DO

[[midPt.shade.xn, midPt.shade.yn, midPt.shade.zn]] ← Add[

[midPt.shade.xn, midPt.shade.yn, midPt.shade.zn],

Cross[midTangents[i].t1, midTangents[i+1].t1]

];

ENDLOOP;

[[midPt.shade.xn, midPt.shade.yn, midPt.shade.zn]] ← Nmlize[

[midPt.shade.xn, midPt.shade.yn, midPt.shade.zn]

];

FOR i: NAT IN [0..patch.nVtces) DO -- Rebuild midtangents using middle point

midTangents[i].t0 ← GetSlopeVec[

[patch[i].shade.xn, patch[i].shade.yn, patch[i].shade.zn],

DiffPosns[midPt.coord, patch[i].coord]

];

midTangents[i].t1 ← GetSlopeVec[

[midPt.shade.xn, midPt.shade.yn, midPt.shade.zn],

DiffPosns[patch[i].coord, midPt.coord]

];

ENDLOOP;

}

ELSE {

midPt.shade.xn ← midPt.shade.xn / loopEnd;

midPt.shade.yn ← midPt.shade.yn / loopEnd;

midPt.shade.zn ← midPt.shade.zn / loopEnd;

};

IF lerpProc # NIL AND midPt.aux # NIL THEN { -- get aux. info from supplied proc

data: LORA ← LIST[midPt.aux, midPt.aux, NEW[REAL ← 1.0/loopEnd], NEW[REAL 𡤀.0]];

midPt ← lerpProc[ NIL, midPt, data];

};

{ OPEN midPt.coord; clip ← ShapeUtilities.GetClipCodeForPt[context, [ ex, ey, ez] ];

IF clip = NoneOut

THEN [ [sx, sy, sz] ] ← ShapeUtilities.XfmPtToDisplay[ context, [ex, ey, ez], shape ];

};

midPt.props ← patch[0].props;

midPt.props ← PutProp[ midPt.props, $Tangents, midTangents ];

};

TriangleDisplay: PROC[ context: REF Context, p: REF Patch, level: NAT, tol: REAL] ~ {

Recursively divide triangular patches to straight edges, then display

subP: REF PatchSequence ← NIL;

IF context.stopMe^ THEN RETURN[]; -- shut down if stop signal received

IF p.dir = undetermined AND p.type = $PolygonWithTangents

THEN [] ← TriangleTngsBackFacing[p]; -- backface test

IF ( p.clipState # out ) AND ( NOT p.oneSided OR NOT p.dir = back ) THEN {

IF level < recurseLimit THEN subP ← SubdivideTriangle[context, p, level, tol];

IF subP = NIL

THEN { -- recursion limit hit or edges all straight

IF showLines THEN p.type ← $PolyLine ELSE p.type ← $ConvexPolygon;

ShapeUtilities.ShadePoly[context, p];

[p] ← SurfaceRender.OutputPolygon[context, p]; -- display

}

ELSE {

subP ← PatchDepthSort[ context, subP ]; -- sort to display order

TriangleDisplay[context, subP[0], level+1, tol];

TriangleDisplay[context, subP[1], level+1, tol];

TriangleDisplay[context, subP[2], level+1, tol];

TriangleDisplay[context, subP[3], level+1, tol];

};

IF p # NIL THEN ShapeUtilities.ReleasePatch[p]; -- end of life for patch

};

SubdivideTriangle: PROC[context: REF Context, p: REF Patch, level: NAT, tol: REAL]
RETURNS[REF PatchSequence] ~ {

Divide triangular patch into four subtriangles

shape: REF ShapeInstance ← NARROW[ GetProp[p.props, $Shape] ];

v0, v1, v2: VertexInfo; flat0, flat1, flat2: BOOLEAN;

t: REF TangentTriple ← NARROW[GetProp[p.props, $Tangents] ];

t00, t01, t10, t11, t20, t21, tm0, tm1, tm2: TangentSet;

outPatch: REF PatchSequence ← NEW[PatchSequence[4]];

IF p.type = $PolygonWithTangents AND t # NIL

THEN { -- get midpoints and edge tangents

[v0, t00, t01, flat0] ← CurveDivideTan[

context, p[0], p[1], t[0].et0, t[0].et1,

GetNmlVec[t[0].et0, p[0]], GetNmlVec[t[0].et1, p[1], TRUE], 0.5, tol ];

[v1, t10, t11, flat1] ← CurveDivideTan[

context, p[1], p[2], t[1].et0, t[1].et1,

GetNmlVec[t[1].et0, p[1]], GetNmlVec[t[1].et1, p[2], TRUE], 0.5, tol];

[v2, t20, t21, flat2] ← CurveDivideTan[

context, p[2], p[0], t[2].et0, t[2].et1,

GetNmlVec[t[2].et0, p[2]], GetNmlVec[t[2].et1, p[0], TRUE], 0.5, tol];

get inner edge tangents based on midpoints

tm0.et0 ← GetSlopeVec[ [v0.shade.exn, v0.shade.eyn, v0.shade.ezn],
DiffPosns[v1.coord, v0.coord, $Eye] ];

tm0.et1 ← GetSlopeVec[ [v1.shade.exn, v1.shade.eyn, v1.shade.ezn],
DiffPosns[v0.coord, v1.coord, $Eye] ];

tm1.et0 ← GetSlopeVec[ [v1.shade.exn, v1.shade.eyn, v1.shade.ezn],
DiffPosns[v2.coord, v1.coord, $Eye] ];

tm1.et1 ← GetSlopeVec[ [v2.shade.exn, v2.shade.eyn, v2.shade.ezn],
DiffPosns[v1.coord, v2.coord, $Eye] ];

tm2.et0 ← GetSlopeVec[ [v2.shade.exn, v2.shade.eyn, v2.shade.ezn],
DiffPosns[v0.coord, v2.coord, $Eye] ];

tm2.et1 ← GetSlopeVec[ [v0.shade.exn, v0.shade.eyn, v0.shade.ezn],
DiffPosns[v2.coord, v0.coord, $Eye] ];

}

ELSE {

[v0, flat0] ← TriangleCurveDivideNml[context, p[0], p[1], level, tol];

[v1, flat1] ← TriangleCurveDivideNml[context, p[1], p[2], level, tol];

[v2, flat2] ← TriangleCurveDivideNml[context, p[2], p[0], level, tol];

};

IF flat0 AND flat1 AND flat2 AND stopIfStraight THEN RETURN[NIL]; -- if all straight, done

{ -- Reverse mid-normals if on wrong side of triangle plane by > 30 deg.

normal: Triple ← Nmlize[ Cross[

DiffPosns[ p[1].coord, p[0].coord, $Eye ], DiffPosns[ p[2].coord, p[0].coord, $Eye ]

] ];

check: REAL;

check ← Dot[[v0.shade.exn, v0.shade.eyn, v0.shade.ezn], normal ];

IF check < -0.5 THEN [[v0.shade.exn, v0.shade.eyn, v0.shade.ezn]] ←
Negate[[v0.shade.exn, v0.shade.eyn, v0.shade.ezn]];

check ← Dot[[v1.shade.exn, v1.shade.eyn, v1.shade.ezn], normal ];

IF check < -0.5 THEN [[v1.shade.exn, v1.shade.eyn, v1.shade.ezn]] ←
Negate[[v1.shade.exn, v1.shade.eyn, v1.shade.ezn]];

check ← Dot[[v2.shade.exn, v2.shade.eyn, v2.shade.ezn], normal ];

IF check < -0.5 THEN [[v2.shade.exn, v2.shade.eyn, v2.shade.ezn]] ←
Negate[[v2.shade.exn, v2.shade.eyn, v2.shade.ezn]];

};

FOR i: NAT IN [0..4) DO

outPatch[i] ← ShapeUtilities.GetPatch[3]; -- 3 point patch, released by display action

outPatch[i].type ← p.type;

outPatch[i].oneSided ← p.oneSided;

outPatch[i].nVtces ← 3;

outPatch[i].clipState ← p.clipState;

outPatch[i].dir ← p.dir;

outPatch[i].props ← p.props;

ENDLOOP;

{ OPEN v0.coord; clip ← ShapeUtilities.GetClipCodeForPt[context, [ ex, ey, ez] ];

IF clip = NoneOut

THEN [ [sx, sy, sz] ] ← ShapeUtilities.XfmPtToDisplay[ context, [ex, ey, ez], shape ]; };

{ OPEN v1.coord; clip ← ShapeUtilities.GetClipCodeForPt[context, [ ex, ey, ez] ];

IF clip = NoneOut

THEN [ [sx, sy, sz] ] ← ShapeUtilities.XfmPtToDisplay[ context, [ex, ey, ez], shape ]; };

{ OPEN v2.coord; clip ← ShapeUtilities.GetClipCodeForPt[context, [ ex, ey, ez] ];

IF clip = NoneOut

THEN [ [sx, sy, sz] ] ← ShapeUtilities.XfmPtToDisplay[ context, [ex, ey, ez], shape ]; };

outPatch[0][0] ← p[0]; outPatch[0][1] ← v0; outPatch[0][2] ← v2;

outPatch[1][0] ← p[1]; outPatch[1][1] ← v1; outPatch[1][2] ← v0;

outPatch[2][0] ← p[2]; outPatch[2][1] ← v2; outPatch[2][2] ← v1;

outPatch[3][0] ← v0; outPatch[3][1] ← v1; outPatch[3][2] ← v2;

IF p.type = $PolygonWithTangents AND t # NIL THEN {

outPatch[0].props ← PutPropSafely[ outPatch[0].props, $Tangents,
NEW[TangentTriple ← [t00, [tm2.t1, tm2.et1, tm2.t0, tm2.et0], t21] ] ];

outPatch[1].props ← PutPropSafely[ outPatch[1].props, $Tangents,
NEW[TangentTriple ← [t10, [tm0.t1, tm0.et1, tm0.t0, tm0.et0], t01] ] ];

outPatch[2].props ← PutPropSafely[ outPatch[2].props, $Tangents,
NEW[TangentTriple ← [t20, [tm1.t1, tm1.et1, tm1.t0, tm1.et0], t11] ] ];

outPatch[3].props ← PutPropSafely[ outPatch[3].props, $Tangents,
NEW[TangentTriple ← [tm0, tm1, tm2] ] ];

outPatch[3].props ← RemPropSafely[ outPatch[3].props, $Tangents];

outPatch[3].type ← $PolygonWithNormals;

};

FOR i: NAT IN [0..4) DO ShapeUtilities.GetPatchClipState[ outPatch[i] ]; ENDLOOP; --bad!!

outPatch.length ← 4;

RETURN[ outPatch ]; -- return four sub-patches

};

Procedures for expansion of non-planar polygons using normals at vertices

DisplayPatchNmls: PatchProc ~ {

shape: REF ShapeInstance ← NARROW[ GetProp[patch.props, $Shape] ];

patch.type ← $PolygonWithNormals;

SELECT shape.shadingClass.shadingType FROM

$Lines => { [] ← DisplayPatchEdges[context, patch]; RETURN[NIL]; };

ENDCASE;

Do we have texture?

IF shape.shadingClass.texture # NIL THEN {

txtrRange: REF Pair ← NARROW[

GetProp[shape.shadingProps, $TxtrCoordRange]

];

IF txtrRange # NIL -- fix texture seams

THEN MappedAndSolidTexture.AdjustTexture[

patch, shape.shadingClass.texture, txtrRange.x, txtrRange.y

]

ELSE MappedAndSolidTexture.AdjustTexture[patch, shape.shadingClass.texture];

};

patch ← TriangulateAndDisplay[context, patch]; -- make triangles, recursively subdivide

IF patch # NIL THEN ShapeUtilities.ReleasePatch[patch]; -- end of life for patch

RETURN[ NIL ];

};

GetEdgeCurveNmls: PROC[p1, p2: VertexInfo] RETURNS[coeffs: G3dSpline.Coeffs] ~ {

edge: Triple ← DiffPosns[p2.coord, p1.coord, $Object];

pos1: Triple ← [p1.coord.x, p1.coord.y, p1.coord.z];

pos2: Triple ← [p2.coord.x, p2.coord.y, p2.coord.z];

slope1: Triple ← GetSlopeVec[[p1.shade.xn, p1.shade.yn, p1.shade.zn], edge, TRUE];

slope2: Triple ← GetSlopeVec[[p2.shade.xn, p2.shade.yn, p2.shade.zn], edge, TRUE];

coeffs ← G3dSpline.CoeffsFromHermite[[pos1, pos2, slope1, slope2]];

};

TriangleNmlsBackFacing: PROC[p: REF Patch] RETURNS [BOOLEAN] ~ {

Use slopes to make corner triangles and internal hexagon, evaluate at corners of hexagon

FacingFromTrio: PROC[p0, p1, p2: Triple] ~ {

direction: Triple ← Cross[

[p1.x - p0.x, p1.y - p0.y, p1.z - p0.z],

[p2.x - p0.x, p2.y - p0.y, p2.z - p0.z]

];

dotDir: REAL ← Dot[p0 , direction];

IF dotDir > 0.0

THEN back ← TRUE

ELSE IF dotDir < 0.0 THEN front ← TRUE ELSE undetermined ← TRUE;

};

back, front, undetermined: BOOLEAN ← FALSE;

t: REF TangentTriple ← NARROW[ GetProp[p.props, $Tangents] ];

pts: ARRAY [0..9) OF Triple;

FOR i: NAT IN [0..3) DO

pts[i*3] ← [ p[i].coord.ex, p[i].coord.ey, p[i].coord.ez ];

ENDLOOP;

FOR i: NAT IN [0..3) DO

i1: NAT ← i*3+1; i2: NAT ← i*3+2;

pts[i*3+1] ← Add[ pts[i*3], t[i].et0];

pts[i*3+2] ← Add[ pts[((i+1) MOD 3) * 3], t[i].et1];

ENDLOOP;

FOR i: NAT IN [0..3) DO

j: NAT ← i*3; j1: NAT ← j+1; j2: NAT ← (j+8) MOD 9;

FacingFromTrio[ pts[j], pts[j1], pts[j2] ];

FacingFromTrio[ pts[j1], pts[j1+1], pts[j2] ];

FacingFromTrio[ pts[j2], pts[j1], pts[j2-1] ];

ENDLOOP;

IF (back AND front) OR undetermined

THEN p.dir ← undetermined

ELSE IF back

THEN p.dir ← back

ELSE IF front

THEN p.dir ← front

ELSE p.dir ← undetermined;

IF p.dir = back THEN RETURN[TRUE] ELSE RETURN[FALSE];

};

TriangleCurveDivideNml: PROC[ context: REF Context, vtx0, vtx1: VertexInfo,
level: NAT, tol: REAL ]
RETURNS[pt: VertexInfo, flat: BOOLEAN] ~ {

Returns parametric midpoint of curve given by v0-v1

t: REAL ~ 0.5;

t2: REAL ~ 0.25;

t3: REAL ~ 0.125;

b0: REAL ~ 1.0 + 0.0*t - 3.*t2 + 2.*t3; -- value of basis functions at t=1/2

b1: REAL ~ 0.0 + 0.0*t + 3.*t2 - 2.*t3;

b2: REAL ~ 0.0 + 1.0*t - 2.*t2 + 1.*t3;

b3: REAL ~ 0.0 + 0.0*t - 1.*t2 + 1.*t3;

s0: REAL ~ 0.0 - 3.*2.*t + 2.*3.*t2; -- slope of basis functions at t=1/2

s1: REAL ~ 0.0 + 3.*2.*t - 2.*3.*t2;

s2: REAL ~ 1.0 - 2.*2.*t + 1.*3.*t2;

s3: REAL ~ 0.0 - 1.*2.*t + 1.*3.*t2;

pos1, pos2, slope1, slope2, slopeMid: Triple;

shape: REF ShapeInstance ← NARROW[ GetProp[vtx0.props, $Shape] ];

Ensure consistent evaluation for arithmetic stability

v0: VertexInfo ← IF vtx0.coord.x < vtx1.coord.x THEN vtx0 ELSE vtx1;

v1: VertexInfo ← IF vtx0.coord.x < vtx1.coord.x THEN vtx1 ELSE vtx0;

clipStraight, tooShort: BOOLEAN ← FALSE;

IF v1.coord.clip # NoneOut AND v0.coord.clip # NoneOut

THEN clipStraight ← TRUE

ELSE IF v0.coord.clip # NoneOut

THEN clipStraight ← TooClose[context, v1.coord, v0.coord.clip, tol]

ELSE IF v1.coord.clip # NoneOut

THEN clipStraight ← TooClose[context, v0.coord, v1.coord.clip, tol];

{ edge: Triple ← DiffPosns[v1.coord, v0.coord, $Eye];

IF Length[edge] <= ScanConvert.justNoticeable

THEN tooShort ← TRUE

ELSE {

slope1 ← GetSlopeVec[[v0.shade.exn, v0.shade.eyn, v0.shade.ezn], edge, TRUE];

slope2 ← GetSlopeVec[[v1.shade.exn, v1.shade.eyn, v1.shade.ezn], edge, TRUE];

};

pos1 ← [v0.coord.ex, v0.coord.ey, v0.coord.ez];

pos2 ← [v1.coord.ex, v1.coord.ey, v1.coord.ez];

IF clipStraight OR tooShort OR EdgeStraight[context, v0, v1, slope1, slope2, tol]

THEN { -- straight edge, average endpoints for midpoint

pt.coord.ex ← (pos1.x + pos2.x) / 2; pt.shade.exn ← (v0.shade.exn + v1.shade.exn) / 2;

pt.coord.ey ← (pos1.y + pos2.y) / 2; pt.shade.eyn ← (v0.shade.eyn + v1.shade.eyn) / 2;

pt.coord.ez ← (pos1.z + pos2.z) / 2; pt.shade.ezn ← (v0.shade.ezn + v1.shade.ezn) / 2;

flat ← TRUE;

}

ELSE { -- not straight, evaluate curve

slopeMid.x ← pos1.x*s0 + pos2.x*s1 + slope1.x*s2 + slope2.x*s3;

slopeMid.y ← pos1.y*s0 + pos2.y*s1 + slope1.y*s2 + slope2.y*s3;

slopeMid.z ← pos1.z*s0 + pos2.z*s1 + slope1.z*s2 + slope2.z*s3;

pt.coord.ex ← pos1.x*b0 + pos2.x*b1 + slope1.x*b2 + slope2.x*b3;

pt.coord.ey ← pos1.y*b0 + pos2.y*b1 + slope1.y*b2 + slope2.y*b3;

pt.coord.ez ← pos1.z*b0 + pos2.z*b1 + slope1.z*b2 + slope2.z*b3;

[[pt.shade.exn, pt.shade.eyn, pt.shade.ezn]] ← Add[

Do with both ends to get consistent mid normal, curve is likely to be non planar

Nmlize[GetSlopeVec[slopeMid, [v0.shade.exn, v0.shade.eyn, v0.shade.ezn], TRUE]],

Nmlize[GetSlopeVec[slopeMid, [v1.shade.exn, v1.shade.eyn, v1.shade.ezn], TRUE]]

];

flat ← FALSE;

};

pt.shade.r ← (v0.shade.r + v1.shade.r) / 2;

pt.shade.g ← (v0.shade.g + v1.shade.g) / 2;

pt.shade.b ← (v0.shade.b + v1.shade.b) / 2;

pt.shade.t ← (v0.shade.t + v1.shade.t) / 2;

IF shape.shadingClass.texture # NIL THEN { -- for solid textures

lerpProc: VertexInfoProc ← shape.shadingClass.lerpVtxAux;

pos1 ← [v0.coord.x, v0.coord.y, v0.coord.z];

pos2 ← [v1.coord.x, v1.coord.y, v1.coord.z];

SELECT shape.class.type FROM

$PolygonWithNormals => {

edge: Triple ← DiffPosns[v1.coord, v0.coord, $Object];

slope1 ← GetSlopeVec[[v0.shade.xn, v0.shade.yn, v0.shade.zn], edge, TRUE];

slope2 ← GetSlopeVec[[v1.shade.xn, v1.shade.yn, v1.shade.zn], edge, TRUE];

};

ENDCASE => SIGNAL ThreeDBasics.Error[[$Unimplemented, "Unknown surface type"]];

IF clipStraight OR EdgeStraight[context, v0, v1, slope1, slope2, tol]

THEN { -- straight edge, average endpoints for midpoint

pt.coord.x ← (pos1.x + pos2.x) / 2; pt.shade.xn ← (v0.shade.xn + v1.shade.xn) / 2;

pt.coord.y ← (pos1.y + pos2.y) / 2; pt.shade.yn ← (v0.shade.yn + v1.shade.yn) / 2;

pt.coord.z ← (pos1.z + pos2.z) / 2; pt.shade.zn ← (v0.shade.zn + v1.shade.zn) / 2;

}

ELSE { -- not straight, evaluate curve

slopeMid.x ← pos1.x*s0 + pos2.x*s1 + slope1.x*s2 + slope2.x*s3;

slopeMid.y ← pos1.y*s0 + pos2.y*s1 + slope1.y*s2 + slope2.y*s3;

slopeMid.z ← pos1.z*s0 + pos2.z*s1 + slope1.z*s2 + slope2.z*s3;

pt.coord.x ← pos1.x*b0 + pos2.x*b1 + slope1.x*b2 + slope2.x*b3;

pt.coord.y ← pos1.y*b0 + pos2.y*b1 + slope1.y*b2 + slope2.y*b3;

pt.coord.z ← pos1.z*b0 + pos2.z*b1 + slope1.z*b2 + slope2.z*b3;

[[pt.shade.xn, pt.shade.yn, pt.shade.zn]] ← Add[

Do with both ends to get stable mid normal, must be a better way

GetSlopeVec[slopeMid, [v0.shade.xn, v0.shade.yn, v0.shade.zn], TRUE],

GetSlopeVec[slopeMid, [v1.shade.xn, v1.shade.yn, v1.shade.zn], TRUE]

];

};

IF lerpProc # NIL AND v0.aux # NIL THEN { -- get auxiliary info from supplied proc

data: LORA ← LIST[ v0.aux, v1.aux, NEW[REAL ← 0.5], NEW[REAL ← 0.5] ];

pt ← lerpProc[ NIL, pt, data]; -- average, for lack of better strategy

};

pt.props ← vtx0.props;

};

Procedures for expansion of non-planar polygons using tangent vectors at vertices

DisplayPatchTngs: PatchProc ~ {

shape: REF ShapeInstance ← NARROW[ GetProp[patch.props, $Shape] ];

SELECT shape.shadingClass.shadingType FROM

$Lines => { [] ← DisplayPatchEdges[context, patch]; RETURN[NIL]; };

ENDCASE;

patch.type ← $PolygonWithTangents;

IF data = NIL

THEN {

patchNo: NAT ← NARROW[ GetProp[patch.props, $PatchNo], REF NAT ]^;

tangents: REF TangentSeqSeq ← NARROW[ GetProp[shape.fixedProps, $PatchTangents] ];

patch ← TriangulateAndDisplay[ context, patch, tangents[patchNo] ]; -- subdivide proc.

}

ELSE {

tangents: REF TangentSeq ← NARROW[ data ];

patch ← TriangulateAndDisplay[ context, patch, tangents ]; -- subdivide proc.

};

IF patch # NIL THEN ShapeUtilities.ReleasePatch[patch]; -- end of life for patch

RETURN[ NIL ];

};

ValidatePolyWTangents: ShapeProc ~ {

PROC[context: REF Context, shape: REF ShapeInstance, data: REF] RETURNS[REF ShapeInstance];

doEyeSpace: BOOLEAN ← shape.vtcesInValid; -- grab before reset by ValidatePatchPoly

shape ← ValidatePatchPoly[context, shape]; -- Update shading and transform matrices

IF GetProp[shape.fixedProps, $PatchTangents] = NIL

THEN shape ← GetTangents[context, shape]; -- calculate tangent vectors if not read in

IF doEyeSpace AND shape.clipState # out THEN {

xfm: Xfm3D ← G3dMatrix.Mul[shape.position, context.eyeSpaceXfm];

tangent: REF TangentSeqSeq ←NARROW[GetProp[shape.fixedProps, $PatchTangents]];

FOR i: NAT IN [0..shape.numSurfaces) DO -- transform tangent vectors

FOR j: NAT IN [0..tangent[i].length) DO OPEN tangent[i][j];

[ et0 ] ← G3dMatrix.TransformVec[ t0, xfm];

[ et1 ] ← G3dMatrix.TransformVec[ t1, xfm];

ENDLOOP;

};

RETURN[ shape ];

};

GetEdgeCurveTngs: PROC[p1, p2: VertexInfo, tangent: TangentSet]
RETURNS[coeffs: G3dSpline.Coeffs] ~ {

b0, b1, b2, b3: Triple;

[b0, b1, b2, b3] ← TngsToBezKnots[ p1, p2, tangent ];

coeffs ← G3dSpline.CoeffsFromBezier[ [b0, b1, b2, b3] ];

};

TngsToBezKnots: PROC[p1, p2: VertexInfo, tangent: TangentSet]
RETURNS[b0, b1, b2, b3: Triple] ~ {

Convert endpoints with tangents to Bezier knots

edgeDir: Triple;

b0 ← [ p1.coord.x, p1.coord.y, p1.coord.z ];

b3 ← [ p2.coord.x, p2.coord.y, p2.coord.z ];

edgeDir ← Sub3[b3, b0];

b1 ← Add[ b0, ScaleTangent[tangent.t0, edgeDir] ];

b2 ← Add[ b3, ScaleTangent[tangent.t1, Negate[edgeDir]] ];

};

TriangleTngsBackFacing: PROC[p: REF Patch] RETURNS [BOOLEAN] ~ {

Use slopes to make corner triangles and internal hexagon, evaluate at corners of hexagon

FacingFromTrio: PROC[p0, p1, p2: Triple] ~ {

direction: Triple ← Cross[

[p1.x - p0.x, p1.y - p0.y, p1.z - p0.z],

[p2.x - p0.x, p2.y - p0.y, p2.z - p0.z]

];

dotDir: REAL ← Dot[p0 , direction];

IF dotDir > 0.0

THEN back ← TRUE

ELSE IF dotDir < 0.0 THEN front ← TRUE ELSE undetermined ← TRUE;

};

back, front, undetermined: BOOLEAN ← FALSE;

t: REF TangentTriple ← NARROW[ GetProp[p.props, $Tangents] ];

pts: ARRAY [0..9) OF Triple;

FOR i: NAT IN [0..3) DO

pts[i*3] ← [ p[i].coord.ex, p[i].coord.ey, p[i].coord.ez ];

ENDLOOP;

FOR i: NAT IN [0..3) DO

i1: NAT ← i*3+1; i2: NAT ← i*3+2;

pts[i*3+1] ← Add[ pts[i*3], t[i].et0];

pts[i*3+2] ← Add[ pts[((i+1) MOD 3) * 3], t[i].et1];

ENDLOOP;

FOR i: NAT IN [0..3) DO

j: NAT ← i*3; j1: NAT ← j+1; j2: NAT ← (j+8) MOD 9;

FacingFromTrio[ pts[j], pts[j1], pts[j2] ];

FacingFromTrio[ pts[j1], pts[j1+1], pts[j2] ];

FacingFromTrio[ pts[j2], pts[j1], pts[j2-1] ];

ENDLOOP;

IF (back AND front) OR undetermined

THEN p.dir ← undetermined

ELSE IF back

THEN p.dir ← back

ELSE IF front

THEN p.dir ← front

ELSE p.dir ← undetermined;

IF p.dir = back THEN RETURN[TRUE] ELSE RETURN[FALSE];

};

NmlizeTangentSet: PROC[v0, v1: VertexInfo, tangent: TangentSet]
RETURNS[TangentSet] ~ {

Convert endpoints with tangents to Properly scaled tangents

ep0: Triple ← [ v0.coord.ex, v0.coord.ey, v0.coord.ez ];

ep1: Triple ← [ v1.coord.ex, v1.coord.ey, v1.coord.ez ];

p0: Triple ← [ v0.coord.x, v0.coord.y, v0.coord.z ];

p1: Triple ← [ v1.coord.x, v1.coord.y, v1.coord.z ];

edgeDir: Triple ← Sub3[p1, p0];

t0: Triple ← ScaleTangent[ tangent.t0, edgeDir ];

t1: Triple ← ScaleTangent[ tangent.t1, Negate[edgeDir] ];

et0, et1: Triple;

edgeDir ← Sub3[ep1, ep0];

et0 ← ScaleTangent[ tangent.et0, edgeDir ];

et1 ← ScaleTangent[ tangent.et1, Negate[edgeDir] ];

RETURN[ [t0, et0, t1, et1] ];

};

IsStraight: PROC[context: REF Context, p0, p1, s0, s1: Triple, tol: REAL] RETURNS[BOOLEAN] ~{

DistOffEdge: PROC[v: Triple, line: Ray] RETURNS[REAL] ~ {

ptOnEdge: Triple ← ShapeUtilities.XfmPtToDisplay[

context, G3dVector.NearestToLine[line, v]

];

vs: Triple ← ShapeUtilities.XfmPtToDisplay[ context, v ];

RETURN[ RealFns.SqRt[ Sqr[ptOnEdge.x - vs.x] + Sqr[ptOnEdge.y - vs.y] ] ];

};

line: Ray ← [ p0, Sub3[p1, p0] ];

Get screen distance of inner knots from edge formed by outer knots

dist0: REAL ← DistOffEdge[Add[p0, s0], line];

dist1: REAL ← DistOffEdge[Add[p1, s1], line];

IF dist0 > tol OR dist1 > tol THEN RETURN[FALSE] ELSE RETURN[TRUE];

};

CurveDivideTan: PROC[ context: REF Context, vtx0, vtx1: VertexInfo,
slope1, slope2, offst1, offst2: Triple, parameter, tol: REAL ]
RETURNS[ pt: VertexInfo, t0, t1: TangentSet, flat: BOOLEAN ] ~ {

Returns point on curve given by v0-v1 and tangents and parameter

p1: REAL ← 1.0 - parameter; p2: REAL ← parameter;

pos1, pos2, edge, oPt: Triple;

shape: REF ShapeInstance ← NARROW[ GetProp[vtx0.props, $Shape] ];

lerpProc: VertexInfoProc ← IF shape # NIL THEN shape.shadingClass.lerpVtxAux ELSE NIL;

v0: VertexInfo ← vtx0;

v1: VertexInfo ← vtx1;

clipStraight, tooShort: BOOLEAN ← FALSE;

IF v1.coord.clip # NoneOut AND v0.coord.clip # NoneOut -- not a good test!!

THEN clipStraight ← TRUE

ELSE IF v0.coord.clip # NoneOut

THEN clipStraight ← TooClose[context, v1.coord, v0.coord.clip, tol]

ELSE IF v1.coord.clip # NoneOut

THEN clipStraight ← TooClose[context, v0.coord, v1.coord.clip, tol];

edge ← DiffPosns[v1.coord, v0.coord, $Eye];

IF Length[edge] <= ScanConvert.justNoticeable THEN tooShort ← TRUE;

pos1 ← [v0.coord.ex, v0.coord.ey, v0.coord.ez];

pos2 ← [v1.coord.ex, v1.coord.ey, v1.coord.ez];

IF clipStraight OR tooShort OR IsStraight[ context, pos1, pos2, slope1, slope2, tol ]

THEN { -- straight edge, average endpoints for midpoint

[[pt.coord.ex, pt.coord.ey, pt.coord.ez]] ← Add[ Mul[pos1, p1], Mul[pos2, p2] ];

t0.et0 ← Mul[ Sub3[pos2, pos1], p2/3.0]; t1.et0 ← Mul[ Sub3[pos2, pos1], p1/3.0];

t0.et1 ← Negate[ t0.et0 ]; t1.et1 ← Negate[ t1.et0 ];

oPt ← Add[ Mul[Add[pos1, offst1], p1], Mul[Add[pos2, offst2], p2] ];

flat ← TRUE;

}

ELSE { -- not straight, evaluate midpoint by subdivision

b0: Triple ← pos1; b3: Triple ← pos2;

b1: Triple ← Add[pos1, slope1]; b2: Triple ← Add[pos2, slope2];

m01, m12, m23, mm0, mm1: Triple;

m01 ← Add[Mul[b0, p1], Mul[b1, p2]];

m12 ← Add[Mul[b1, p1], Mul[b2, p2]];

m23 ← Add[Mul[b2, p1], Mul[b3, p2]];

mm0 ← Add[Mul[m01, p1], Mul[m12, p2]]; mm1 ← Add[Mul[m23, p1], Mul[m12, p2]];

[[pt.coord.ex, pt.coord.ey, pt.coord.ez]] ← Add[ Mul[mm1, p1], Mul[mm0, p2] ];

t0.et0 ← Mul[ slope1, p2 ]; t0.et1 ← Sub3[mm0, [pt.coord.ex, pt.coord.ey, pt.coord.ez] ];

t1.et0 ← Sub3[mm1, [pt.coord.ex, pt.coord.ey, pt.coord.ez] ]; t1.et1 ← Mul[ slope2, p1 ];

b0 ← Add[pos1, offst1]; b3 ← Add[pos2, offst2]; -- get offset midpoint

b1 ← Add[b0, slope1]; b2 ← Add[b3, slope2];

m01 ← Add[Mul[b0, p1], Mul[b1, p2]];

m12 ← Add[Mul[b1, p1], Mul[b2, p2]];

m23 ← Add[Mul[b2, p1], Mul[b3, p2]];

mm0 ← Add[Mul[m01, p1], Mul[m12, p2]]; mm1 ← Add[Mul[m23, p1], Mul[m12, p2]];

oPt ← Add[ Mul[mm1, p1], Mul[mm0, p2] ];

flat ← FALSE;

};

[[pt.shade.exn, pt.shade.eyn, pt.shade.ezn]] ← Nmlize[

Cross[ Sub3[ oPt, [pt.coord.ex, pt.coord.ey, pt.coord.ez] ], t1.et0 ]

];

pt.shade.r ← p1 * v0.shade.r + p2 * v1.shade.r;

pt.shade.g ← p1 * v0.shade.g + p2 * v1.shade.g;

pt.shade.b ← p1 * v0.shade.b + p2 * v1.shade.b;

pt.shade.t ← p1 * v0.shade.t + p2 * v1.shade.t;

IF shape.shadingClass.texture # NIL THEN { -- for solid textures

lerpProc: VertexInfoProc ← shape.shadingClass.lerpVtxAux;

pos1 ← [v0.coord.x, v0.coord.y, v0.coord.z];

pos2 ← [v1.coord.x, v1.coord.y, v1.coord.z];

SELECT shape.class.type FROM

$PolygonWithTangents => {

edge: Triple ← DiffPosns[v1.coord, v0.coord, $Object];

slope1 ← IF tan.t0 # nullTriple

THEN tan.t0

ELSE GetSlopeVec[ [v0.shade.xn, v0.shade.yn, v0.shade.zn], edge ];

slope2 ← IF tan.t1 # nullTriple

THEN tan.t1

ELSE GetSlopeVec[ [v1.shade.xn, v1.shade.yn, v1.shade.zn], Negate[edge] ];

};

ENDCASE => SIGNAL ThreeDBasics.Error[[$Unimplemented, "Unknown surface type"]];

pt.shade.xn ← (v0.shade.xn + v1.shade.xn) / 2;

pt.shade.yn ← (v0.shade.yn + v1.shade.yn) / 2;

pt.shade.zn ← (v0.shade.zn + v1.shade.zn) / 2;

IF flat

THEN { -- straight edge, average endpoints for midpoint

pt.coord.x ← (pos1.x + pos2.x) / 2;

pt.coord.y ← (pos1.y + pos2.y) / 2;

pt.coord.z ← (pos1.z + pos2.z) / 2;

}

ELSE { -- not straight, evaluate curve

b0: Triple ← pos1; b3: Triple ← pos2;

b1: Triple ← Add[pos1, slope1];

b2: Triple ← Add[pos2, slope2];

m01, m12, m23, mm0, mm1: Triple;

m01.x ← (b0.x + b1.x)/2; m01.y ← (b0.y + b1.y)/2; m01.z ← (b0.z + b1.z)/2;

m12.x ← (b1.x + b2.x)/2; m12.y ← (b1.y + b2.y)/2; m12.z ← (b1.z + b2.z)/2;

m23.x ← (b2.x + b3.x)/2; m23.y ← (b2.y + b3.y)/2; m23.z ← (b2.z + b3.z)/2;

mm0.x ← (m01.x+m12.x)/2; mm0.y ← (m01.y+m12.y)/2; mm0.z ← (m01.z+m12.z)/2;

mm1.x ← (m23.x+m12.x)/2; mm1.y ← (m23.y+m12.y)/2; mm1.z ← (m23.z+m12.z)/2;

pt.coord.x ← (mm1.x + mm0.x) / 2;

pt.coord.y ← (mm1.y + mm0.y) / 2;

pt.coord.z ← (mm1.z + mm0.z) / 2;

t0.t0 ← [ slope1.x / 2, slope1.y / 2, slope1.z / 2 ];

t0.t1 ← [ mm0.x - pt.coord.x, mm0.y - pt.coord.y, mm0.z - pt.coord.z ];

t1.t0 ← [ mm1.x - pt.coord.x, mm1.y - pt.coord.y, mm1.z - pt.coord.z ];

t1.t1 ← [ slope2.x / 2, slope2.y / 2, slope2.z / 2 ];

};

IF lerpProc # NIL AND v0.aux # NIL THEN { -- get auxiliary info from supplied proc

data: LORA ← LIST[ v0.aux, v1.aux, NEW[REAL ← 0.5], NEW[REAL ← 0.5] ];

pt ← lerpProc[ NIL, pt, data]; -- average, for lack of better strategy

};

pt.props ← vtx0.props;

};

Procedures for tensor product quadrilaterals using tangent vectors at vertices

DisplayPatchTnsr: PatchProc ~ {

shape: REF ShapeInstance ← NARROW[ GetProp[patch.props, $Shape] ];

SELECT shape.shadingClass.shadingType FROM

$Lines => { [] ← DisplayPatchEdges[context, patch]; RETURN[NIL]; };

ENDCASE;

patch.type ← $PolygonToTnsrPatch;

IF data = NIL

THEN {

patchNo: NAT ← NARROW[ GetProp[patch.props, $PatchNo], REF NAT ]^;

tangents: REF TangentSeqSeq ← NARROW[ GetProp[shape.fixedProps, $PatchTangents] ];

patch ← SubDivideTnsr[ context, patch, tangents[patchNo] ]; -- subdivide proc.

}

ELSE {

tangents: REF TangentSeq ← NARROW[ data ];

patch ← SubDivideTnsr[ context, patch, tangents ]; -- subdivide proc.

};

IF patch # NIL THEN ShapeUtilities.ReleasePatch[patch]; -- end of life for patch

RETURN[ NIL ];

};

SubDivideTnsr: PatchProc ~ {

Divide polygon into quadrilateral and triangular patches, depth sort, divide triangles into quadrilaterals then call QuadrilateralDisplay on each one

tol: REAL ← IF context.antiAliasing THEN maxDeviation ELSE maxJaggyDeviation;

tangents: REF TangentSeq ← NARROW[ data ];

IF patch.nVtces < 3 THEN SIGNAL ThreeDBasics.Error[[$MisMatch, "Not enough vertices"]];

IF patch.nVtces = 3

THEN {

patch.props ← PutPropSafely[

patch.props, $Tangents,

NEW[TangentTriple ← [

NmlizeTangentSet[ patch[0], patch[1], tangents[0] ],

NmlizeTangentSet[ patch[1], patch[2], tangents[1] ],

NmlizeTangentSet[ patch[2], patch[0], tangents[2] ]

]]

];

TnsrTriangleDivide[context, patch, tol];

}

ELSE IF patch.nVtces > 4 THEN {

outPatch: REF PatchSequence ← NEW [PatchSequence[patch.nVtces]];

midPt: VertexInfo ← GetCenterPt[context, patch, tangents];

midTangents: REF TangentSeq ← NARROW[

GetProp[midPt.props, $Tangents]

];

FOR i: NAT IN [0..patch.nVtces) DO

j: NAT ← (i + 1) MOD patch.nVtces; -- next vertex

outPatch[i] ← ShapeUtilities.GetPatch[3]; -- released by display action

outPatch[i].type ← patch.type;

outPatch[i].oneSided ← patch.oneSided;

outPatch[i].nVtces ← 3;

outPatch[i].clipState ← patch.clipState;

outPatch[i].dir ← undetermined;

outPatch[i].props ← patch.props;

outPatch[i][0] ← patch[i];

outPatch[i][1] ← patch[(i+1) MOD patch.nVtces];

outPatch[i][2] ← midPt;

outPatch[i].props ← PutPropSafely[

outPatch[i].props, $Tangents,

NEW[TangentTriple ← [

NmlizeTangentSet[ outPatch[i][0], outPatch[i][1], tangents[i] ], -- orig. edge

midTangents[j], -- in to middle, from next vertex

[ t0: midTangents[i].t1, et0: midTangents[i].et1, -- back out to current vertex
t1: midTangents[i].t0, et1: midTangents[i].et0 ]

]]

];

IF outPatch[i].clipState # in THEN ShapeUtilities.GetPatchClipState[ outPatch[i] ];

ENDLOOP;

outPatch.length ← patch.nVtces;

outPatch ← PatchDepthSort[ context, outPatch ]; -- sort to depth order

FOR i: NAT IN [0..patch.nVtces) DO

TnsrTriangleDivide[context, outPatch[i], tol];

ENDLOOP;

}

ELSE {

patch.props ← PutPropSafely[

patch.props, $Tangents,

NEW[TangentQuad ← [

NmlizeTangentSet[ patch[0], patch[1], tangents[0] ],

NmlizeTangentSet[ patch[1], patch[2], tangents[1] ],

NmlizeTangentSet[ patch[2], patch[3], tangents[2] ],

NmlizeTangentSet[ patch[3], patch[0], tangents[3] ]

]]

];

TnsrQuadDisplay[context, patch, 0, tol];

};

patch ← NIL; -- nil out patch so it won't be returned to cache by caller

RETURN[patch];

};

TnsrQuadDisplay: PROC[ context: REF Context, p: REF Patch, level: NAT, tol: REAL] ~ {

Recursively divide quadrilateral patches to straight edges, then display

subP: REF PatchSequence ← NIL;

IF context.stopMe^ THEN RETURN[]; -- shut down if stop signal received

IF p.dir = undetermined THEN [] ← TnsrQuadBackFacing[p]; -- backface test

IF ( p.clipState # out ) AND ( NOT p.oneSided OR NOT p.dir = back ) THEN {

IF level < recurseLimit THEN subP ← SubdivideTnsrQuad[context, p, level, tol];

IF subP = NIL

THEN { -- recursion limit hit or edges all straight

IF showLines THEN p.type ← $PolyLine ELSE p.type ← $ConvexPolygon;

ShapeUtilities.ShadePoly[context, p];

[p] ← SurfaceRender.OutputPolygon[context, p]; -- display

}

ELSE {

subP ← PatchDepthSort[ context, subP ]; -- sort to display order

TnsrQuadDisplay[context, subP[0], level+1, tol];

TnsrQuadDisplay[context, subP[1], level+1, tol];

TnsrQuadDisplay[context, subP[2], level+1, tol];

TnsrQuadDisplay[context, subP[3], level+1, tol];

};

IF p # NIL THEN ShapeUtilities.ReleasePatch[p]; -- end of life for patch

};

TnsrTriangleDivide: PROC[ context: REF Context, p: REF Patch, tol: REAL] ~ {

Divide triangular patch into three subquadrilaterals and send to display

shape: REF ShapeInstance ← NARROW[ GetProp[p.props, $Shape] ];

v0, v1, v2, vCtr, vCtr1, vCtr2, vCtr3: VertexInfo; flat0, flat1, flat2: BOOLEAN;

t: REF TangentTriple ← NARROW[GetProp[p.props, $Tangents] ];

t00, t01, t10, t11, t20, t21, tm0, tm1, tm2: TangentSet;

outPatch: REF PatchSequence ← NEW[PatchSequence[3]];

Find midpoints and midslopes for each side

[v0, t00, t01, flat0] ← CurveDivideTan[

context, p[0], p[1], t[0].et0, t[0].et1,

GetNmlVec[t[0].et0, p[0]], GetNmlVec[t[0].et1, p[1], TRUE], 0.5, tol ];

[v1, t10, t11, flat1] ← CurveDivideTan[

context, p[1], p[2], t[1].et0, t[1].et1,

GetNmlVec[t[1].et0, p[1]], GetNmlVec[t[1].et1, p[2], TRUE], 0.5, tol];

[v2, t20, t21, flat2] ← CurveDivideTan[

context, p[2], p[0], t[2].et0, t[2].et1,

GetNmlVec[t[2].et0, p[2]], GetNmlVec[t[2].et1, p[0], TRUE], 0.5, tol];

IF flat0 AND flat1 AND flat2 AND stopIfStraight -- all straight? then done

THEN TnsrQuadDisplay[context, p, recurseLimit, tol]; -- display as polygon

Get inner edges from midpoint to opposite vertex curves

tm0.et0 ← GetSlopeVec[ [v0.shade.exn, v0.shade.eyn, v0.shade.ezn], Add[t10.et0, t21.et1] ];

tm0.et0 ← ScaleTangent[ tm0.et0, DiffPosns[p[2].coord, v0.coord, $Eye] ];

tm0.et1 ← GetSlopeVec[ [p[2].shade.exn, p[2].shade.eyn, p[2].shade.ezn], Add[t20.et0, t11.et1]];

tm0.et1 ← ScaleTangent[ tm0.et1, DiffPosns[v0.coord, p[2].coord, $Eye] ];

tm1.et0 ← GetSlopeVec[ [v1.shade.exn, v1.shade.eyn, v1.shade.ezn], Add[t20.et0, t01.et1]];

tm1.et0 ← ScaleTangent[ tm1.et0, DiffPosns[p[0].coord, v1.coord, $Eye] ];

tm1.et1 ← GetSlopeVec[ [p[0].shade.exn, p[0].shade.eyn, p[0].shade.ezn], Add[t00.et0, t21.et1]];

tm1.et1 ← ScaleTangent[ tm1.et1, DiffPosns[v1.coord, p[0].coord, $Eye] ];

tm2.et0 ← GetSlopeVec[ [v2.shade.exn, v2.shade.eyn, v2.shade.ezn], Add[t00.et0, t11.et1]];

tm2.et0 ← ScaleTangent[ tm2.et0, DiffPosns[p[1].coord, v2.coord, $Eye] ];

tm2.et1 ← GetSlopeVec[ [p[1].shade.exn, p[1].shade.eyn, p[1].shade.ezn], Add[t10.et0, t01.et1]];

tm2.et1 ← ScaleTangent[ tm2.et1, DiffPosns[v2.coord, p[1].coord, $Eye] ];

Split inner edges at 1/3 point and average for ctr. point

[vCtr1, tm0, , ] ← CurveDivideTan[

context, v0, p[2], tm0.et0, tm0.et1,

GetNmlVec[tm0.et0, v0], GetNmlVec[tm0.et1, p[2], TRUE], 1.0/3.0, tol ];

[vCtr2, tm1, , ] ← CurveDivideTan[

context, v1, p[0], tm1.et0, tm1.et1,

GetNmlVec[tm1.et0, v1], GetNmlVec[tm1.et1, p[0], TRUE], 1.0/3.0, tol ];

[vCtr3, tm2, , ] ← CurveDivideTan[

context, v2, p[1], tm2.et0, tm2.et1,

GetNmlVec[tm2.et0, v2], GetNmlVec[tm2.et1, p[1], TRUE], 1.0/3.0, tol ];

[[vCtr.coord.ex, vCtr.coord.ey, vCtr.coord.ez]] ← Div[ -- average positions

Add[

[vCtr1.coord.ex, vCtr1.coord.ey, vCtr1.coord.ez],

Add[

[vCtr2.coord.ex, vCtr2.coord.ey, vCtr2.coord.ez],

[vCtr3.coord.ex, vCtr3.coord.ey, vCtr3.coord.ez]

]

3.0

];

[[vCtr.shade.exn, vCtr.shade.eyn, vCtr.shade.ezn]] ← Div[ -- average normals

Add[

[vCtr1.shade.exn, vCtr1.shade.eyn, vCtr1.shade.ezn],

Add[

[vCtr2.shade.exn, vCtr2.shade.eyn, vCtr2.shade.ezn],

[vCtr3.shade.exn, vCtr3.shade.eyn, vCtr3.shade.ezn]

]

3.0

];

FOR i: NAT IN [0..3) DO

outPatch[i] ← ShapeUtilities.GetPatch[4]; -- 4 point patch, released by display action

outPatch[i].type ← p.type;

outPatch[i].oneSided ← p.oneSided;

outPatch[i].nVtces ← 4;

outPatch[i].clipState ← p.clipState;

outPatch[i].dir ← p.dir;

outPatch[i].props ← p.props;

ENDLOOP;

{ OPEN v0.coord; clip ← ShapeUtilities.GetClipCodeForPt[context, [ ex, ey, ez] ];

IF clip = NoneOut

THEN [ [sx, sy, sz] ] ← ShapeUtilities.XfmPtToDisplay[ context, [ex, ey, ez], shape ]; };

{ OPEN v1.coord; clip ← ShapeUtilities.GetClipCodeForPt[context, [ ex, ey, ez] ];

IF clip = NoneOut

THEN [ [sx, sy, sz] ] ← ShapeUtilities.XfmPtToDisplay[ context, [ex, ey, ez], shape ]; };

{ OPEN v2.coord; clip ← ShapeUtilities.GetClipCodeForPt[context, [ ex, ey, ez] ];

IF clip = NoneOut

THEN [ [sx, sy, sz] ] ← ShapeUtilities.XfmPtToDisplay[ context, [ex, ey, ez], shape ]; };

{ OPEN vCtr.coord; clip ← ShapeUtilities.GetClipCodeForPt[context, [ ex, ey, ez] ];

IF clip = NoneOut

THEN [ [sx, sy, sz] ] ← ShapeUtilities.XfmPtToDisplay[ context, [ex, ey, ez], shape ]; };

outPatch[0][0] ← p[0]; outPatch[0][1] ← v0; outPatch[0][2] ← vCtr; outPatch[0][3] ← v2;

outPatch[1][0] ← p[1]; outPatch[1][1] ← v1; outPatch[1][2] ← vCtr; outPatch[1][3] ← v0;

outPatch[2][0] ← p[2]; outPatch[2][1] ← v2; outPatch[2][2] ← vCtr; outPatch[2][3] ← v1;

outPatch[0].props ← PutPropSafely[ outPatch[0].props, $Tangents, NEW[TangentQuad ←

[t00, tm0, [tm2.t1, tm2.et1, tm2.t0, tm2.et0], t21] ] ];

outPatch[1].props ← PutPropSafely[ outPatch[1].props, $Tangents, NEW[TangentQuad ←

[t10, tm1, [tm0.t1, tm0.et1, tm0.t0, tm0.et0], t01] ] ];

outPatch[2].props ← PutPropSafely[ outPatch[2].props, $Tangents, NEW[TangentQuad ←

[t20, tm2, [tm1.t1, tm1.et1, tm1.t0, tm1.et0], t11] ] ];

FOR i: NAT IN [0..3) DO ShapeUtilities.GetPatchClipState[ outPatch[i] ]; ENDLOOP; --bad!!

outPatch.length ← 3;

FOR i: NAT IN [0..3) DO TnsrQuadDisplay[ context, outPatch[i], 0, tol ]; ENDLOOP;

};

SubdivideTnsrQuad: PROC[context: REF Context, p: REF Patch, level: NAT, tol: REAL]
RETURNS[REF PatchSequence] ~ {

Divide quadrangular patch into four subquadrangles

shape: REF ShapeInstance ← NARROW[ GetProp[p.props, $Shape] ];

v0, v1, v2, v3, vCtr, vCtr2: VertexInfo; flat0, flat1, flat2, flat3: BOOLEAN;

t: REF TangentQuad ← NARROW[GetProp[p.props, $Tangents] ];

t00, t01, t10, t11, t20, t21, t30, t31, tm0, tm1, tm2, tm3: TangentSet;

outPatch: REF PatchSequence ← NEW[PatchSequence[4]];

Find midpoints and midslopes for each side

[v0, t00, t01, flat0] ← CurveDivideTan[

context, p[0], p[1], t[0].et0, t[0].et1,

GetNmlVec[t[0].et0, p[0]], GetNmlVec[t[0].et1, p[1], TRUE], 0.5, tol ];

[v1, t10, t11, flat1] ← CurveDivideTan[

context, p[1], p[2], t[1].et0, t[1].et1,

GetNmlVec[t[1].et0, p[1]], GetNmlVec[t[1].et1, p[2], TRUE], 0.5, tol];

[v2, t20, t21, flat2] ← CurveDivideTan[

context, p[2], p[3], t[2].et0, t[2].et1,

GetNmlVec[t[2].et0, p[2]], GetNmlVec[t[2].et1, p[3], TRUE], 0.5, tol];

[v3, t30, t31, flat3] ← CurveDivideTan[

context, p[3], p[0], t[3].et0, t[3].et1,

GetNmlVec[t[3].et0, p[3]], GetNmlVec[t[3].et1, p[0], TRUE], 0.5, tol];

IF flat0 AND flat1 AND flat2 AND flat3 AND stopIfStraight -- all straight? then done

THEN RETURN[NIL];

Get inner edge endpoint tangents from opposite midpoints

- first project direction given by endpoint cross-tangents on plane given by normal

- Then scale direction by distance to opposite midpoint

tm0.et0 ← GetSlopeVec[ [v0.shade.exn, v0.shade.eyn, v0.shade.ezn], Add[t10.et0, t31.et1] ];

tm0.et0 ← ScaleTangent[ tm0.et0, DiffPosns[v2.coord, v0.coord, $Eye] ];

tm0.et1 ← GetSlopeVec[ [v2.shade.exn, v2.shade.eyn, v2.shade.ezn], Add[t11.et1, t30.et0] ];

tm0.et1 ← ScaleTangent[ tm0.et1, DiffPosns[v0.coord, v2.coord, $Eye] ];

tm1.et0 ← GetSlopeVec[ [v1.shade.exn, v1.shade.eyn, v1.shade.ezn], Add[t20.et0, t01.et1] ];

tm1.et0 ← ScaleTangent[ tm1.et0, DiffPosns[v3.coord, v1.coord, $Eye] ];

tm1.et1 ← GetSlopeVec[ [v3.shade.exn, v3.shade.eyn, v3.shade.ezn], Add[t21.et1, t00.et0] ];

tm1.et1 ← ScaleTangent[ tm1.et1, DiffPosns[v1.coord, v3.coord, $Eye] ];

tm0.et0 ← GetSlopeVec[ [v0.shade.exn, v0.shade.eyn, v0.shade.ezn],
DiffPosns[v2.coord, v0.coord, $Eye] ];

tm0.et1 ← GetSlopeVec[ [v2.shade.exn, v2.shade.eyn, v2.shade.ezn],
DiffPosns[v0.coord, v2.coord, $Eye] ];

tm1.et0 ← GetSlopeVec[ [v1.shade.exn, v1.shade.eyn, v1.shade.ezn],
DiffPosns[v3.coord, v1.coord, $Eye] ];

tm1.et1 ← GetSlopeVec[ [v3.shade.exn, v3.shade.eyn, v3.shade.ezn],
DiffPosns[v1.coord, v3.coord, $Eye] ];

Get center point, normal and cross tangents

[vCtr, tm0, tm2, ] ← CurveDivideTan[

context, v0, v2, tm0.et0, tm0.et1,

GetNmlVec[tm0.et0, v0], GetNmlVec[tm0.et1, v2, TRUE], 0.5, tol ];

[vCtr2, tm1, tm3, ] ← CurveDivideTan[

context, v1, v3, tm1.et0, tm1.et1,

GetNmlVec[tm1.et0, v1], GetNmlVec[tm1.et1, v3, TRUE], 0.5, tol ];

[[vCtr.coord.ex, vCtr.coord.ey, vCtr.coord.ez]] ← Div[ -- average

Add[

[vCtr.coord.ex, vCtr.coord.ey, vCtr.coord.ez],

[vCtr2.coord.ex, vCtr2.coord.ey, vCtr2.coord.ez]

];

[[vCtr.shade.exn, vCtr.shade.eyn, vCtr.shade.ezn]] ← Nmlize[ Cross[ tm2.et0 , tm3.et0 ] ];

FOR i: NAT IN [0..4) DO

outPatch[i] ← ShapeUtilities.GetPatch[4]; -- 4 point patch, released by display action

outPatch[i].type ← p.type;

outPatch[i].oneSided ← p.oneSided;

outPatch[i].nVtces ← 4;

outPatch[i].clipState ← p.clipState;

outPatch[i].dir ← p.dir;

outPatch[i].props ← p.props;

ENDLOOP;

{ OPEN v0.coord; clip ← ShapeUtilities.GetClipCodeForPt[context, [ ex, ey, ez] ];

IF clip = NoneOut

THEN [ [sx, sy, sz] ] ← ShapeUtilities.XfmPtToDisplay[ context, [ex, ey, ez], shape ]; };

{ OPEN v1.coord; clip ← ShapeUtilities.GetClipCodeForPt[context, [ ex, ey, ez] ];

IF clip = NoneOut

THEN [ [sx, sy, sz] ] ← ShapeUtilities.XfmPtToDisplay[ context, [ex, ey, ez], shape ]; };

{ OPEN v2.coord; clip ← ShapeUtilities.GetClipCodeForPt[context, [ ex, ey, ez] ];

IF clip = NoneOut

THEN [ [sx, sy, sz] ] ← ShapeUtilities.XfmPtToDisplay[ context, [ex, ey, ez], shape ]; };

{ OPEN v3.coord; clip ← ShapeUtilities.GetClipCodeForPt[context, [ ex, ey, ez] ];

IF clip = NoneOut

THEN [ [sx, sy, sz] ] ← ShapeUtilities.XfmPtToDisplay[ context, [ex, ey, ez], shape ]; };

{ OPEN vCtr.coord; clip ← ShapeUtilities.GetClipCodeForPt[context, [ ex, ey, ez] ];

IF clip = NoneOut

THEN [ [sx, sy, sz] ] ← ShapeUtilities.XfmPtToDisplay[ context, [ex, ey, ez], shape ]; };

outPatch[0][0] ← p[0]; outPatch[0][1] ← v0; outPatch[0][2] ← vCtr; outPatch[0][3] ← v3;

outPatch[1][0] ← p[1]; outPatch[1][1] ← v1; outPatch[1][2] ← vCtr; outPatch[1][3] ← v0;

outPatch[2][0] ← p[2]; outPatch[2][1] ← v2; outPatch[2][2] ← vCtr; outPatch[2][3] ← v1;

outPatch[3][0] ← p[3]; outPatch[3][1] ← v3; outPatch[3][2] ← vCtr; outPatch[3][3] ← v2;

IF t # NIL THEN {

outPatch[0].props ← PutPropSafely[ outPatch[0].props, $Tangents, NEW[TangentQuad ←

[t00, tm0, tm3, t31] ] ];

outPatch[1].props ← PutPropSafely[ outPatch[1].props, $Tangents, NEW[TangentQuad ←

[t10, tm1, [tm0.t1, tm0.et1, tm0.t0, tm0.et0], t01] ] ];

outPatch[2].props ← PutPropSafely[ outPatch[2].props, $Tangents, NEW[TangentQuad ←

[t20, [tm2.t1, tm2.et1, tm2.t0, tm2.et0], [tm1.t1, tm1.et1, tm1.t0, tm1.et0], t11] ] ];

outPatch[3].props ← PutPropSafely[ outPatch[3].props, $Tangents, NEW[TangentQuad ←

[t30, [tm3.t1, tm3.et1, tm3.t0, tm3.et0], tm2, t21] ] ];

};

FOR i: NAT IN [0..4) DO ShapeUtilities.GetPatchClipState[ outPatch[i] ]; ENDLOOP; --bad!!

outPatch.length ← 4;

RETURN[ outPatch ]; -- return four sub-patches

};

TnsrQuadBackFacing: PROC[p: REF Patch] RETURNS [BOOLEAN] ~ {

p.dir ← undetermined; -- don't know how to do this yet

IF p.dir = back THEN RETURN[TRUE] ELSE RETURN[FALSE];

};

Procedures for computing tangent vectors at vertices

GetTangents: ShapeProc ~ {

Build endpoint tangents for each edge of a polygon

GetSlope: PROC[normal, edge1, edge2: Triple, reverse: BOOL] RETURNS[slope: Triple] ~ {

Returns a vector normal to the 1st vector and in the plane defined by both vectors

cornerNorm: Triple ← Cross[edge1, edge2];

IF reverse THEN cornerNorm ← Negate[ cornerNorm ];

slope ← Cross[ Cross[normal, edge2], normal ];

IF Length[slope] < .0001 THEN IF Dot[normal, edge2] < 0.0 -- catch degenerate cases

THEN slope ← cornerNorm ELSE slope ← Negate[ cornerNorm ];

IF Dot[ normal, cornerNorm ] < 0.0 THEN

IF Dot[ Nmlize[edge2], Nmlize[normal] ] > Dot[ Nmlize[edge1], Nmlize[normal] ]

THEN slope ← Negate[ slope ]; -- wrong side of plane, high-curvature on one side

SIGNAL ThreeDBasics.Error[[$Unimplemented, "surface ambiguously curved"]];

slope ← ScaleTangent[ slope, edge2 ];

};

nullTriple: Triple ← [0.0, 0.0, 0.0];

surface: REF PtrPatchSequence ← NARROW[shape.surface];

corners: REF CornerSeqSeq;

Pass through polygon structure, getting vertex normals robustly while building corner structure.

corners ← GetNormalsAndDirections[shape]; -- Get robust vertex normals and edge directions

Order contiguous polygons to clockwise around vertex, seen from outside

FOR i: NAT IN [0..corners.length) DO -- sort corners to clockwise order by matching edges

IF corners[i] # NIL THEN corners[i] ← SortVertex[ corners[i] ];

ENDLOOP;

Build tangents at corners around each vertex. By projecting edge directions on plane given by normal

FOR i: NAT IN [0..corners.length) DO

nCorners: NAT ← IF corners[i] # NIL THEN corners[i].length ELSE 0;

outDirs: REF TripleSequence ← NEW[TripleSequence[nCorners]]; -- temp tangents

inDirs: REF TripleSequence ← NEW[TripleSequence[nCorners]];

FOR this: NAT IN [0..nCorners) DO

last: NAT ← (this + nCorners-1) MOD nCorners;

outDirs[this] ← GetSlope[

corners[i][this].normal, corners[i][this].inDir, corners[i][this].outDir,

corners[i][this].concave

];

IF corners[i][last].inVtx = corners[i][this].outVtx -- matches previous corner

THEN inDirs[last] ← outDirs[this] -- copy vector

ELSE inDirs[last] ← GetSlope[ -- open edge, compute vector

corners[i][last].normal, corners[i][last].outDir, corners[i][last].inDir,

NOT corners[i][this].concave

];

ENDLOOP;

FOR this: NAT IN [0..nCorners) DO -- store new tangents

corners[i][this].outDir ← outDirs[this];

corners[i][this].inDir ← inDirs[this];

ENDLOOP;

Make tangents continuous if within 30 degrees of being so. Always make continuous if open edge

FOR i: NAT IN [0..corners.length) DO

IF corners[i] # NIL THEN corners[i] ← FindContinuousEdges[ shape, i, corners[i] ];

ENDLOOP;

{ -- build tangent structure for polygons, using the vertex tangent structure just constructed

tangents: REF TangentSeqSeq ← NEW[ TangentSeqSeq[shape.numSurfaces] ];

FOR i: NAT IN [0..shape.numSurfaces) DO IF surface[i] # NIL THEN {

nVtces: NAT ← surface[i].nVtces;

tangents[i] ← NEW[ TangentSeq[nVtces] ];

FOR cVtx: NAT IN [0..nVtces) DO -- get direction vectors for each edge at vtx.

vtx: NAT ← surface[i].vtxPtr[cVtx]; -- current vertex

nVtx: NAT ← surface[i].vtxPtr[(cVtx + 1) MOD nVtces]; -- other end of edge

Find outgoing direction vector by pointer to opposing vertex

IF corners[vtx][corners[vtx].length-1].inVtx # corners[vtx][0].outVtx -- open edge?

AND corners[vtx][corners[vtx].length-1].inVtx = nVtx -- check last inDir

THEN tangents[i][cVtx].t0 ← corners[vtx][corners[vtx].length-1].inDir

ELSE FOR j: NAT IN [0..corners[vtx].length) DO -- otherwise check all outDirs

IF corners[vtx][j].outVtx = nVtx THEN

{ tangents[i][cVtx].t0 ← corners[vtx][j].outDir; EXIT; };

ENDLOOP;

Find direction vector at other end of edge by looking back from opposing vertex

IF corners[nVtx][corners[nVtx].length-1].inVtx # corners[nVtx][0].outVtx -- open?

AND corners[nVtx][corners[nVtx].length-1].inVtx = vtx -- last inDir

THEN tangents[i][cVtx].t1 ← corners[nVtx][corners[nVtx].length-1].inDir

ELSE FOR j: NAT IN [0..corners[nVtx].length) DO -- otherwise check all outDirs

IF corners[nVtx][j].outVtx = vtx THEN

{ tangents[i][cVtx].t1 ← corners[nVtx][j].outDir; EXIT; };

ENDLOOP;

IF tangents[i][cVtx].t0 = nullTriple OR tangents[i][cVtx].t1 = nullTriple THEN

SIGNAL ThreeDBasics.Error[[$Fatal, "Null tangent vector, bad topology?"]];

ENDLOOP;

tangents[i].length ← nVtces;

};

ENDLOOP;

tangents.length ← shape.numSurfaces;

shape.fixedProps ← PutProp[shape.fixedProps, $PatchTangents, tangents];

};

RETURN[shape];

};

GetNormalsAndDirections: PROC[shape: REF ShapeInstance] RETURNS[REF CornerSeqSeq] ~ {

Get vertex normals robustly ( using robust polygon normal )

Find incoming and outgoing directions for each polygon at a vertex

preNormaled: BOOLEAN ← GetProp[shape.fixedProps, $VertexNormalsInFile] # NIL;

surface: REF PtrPatchSequence ← NARROW[shape.surface];

corners: REF CornerSeqSeq ← NEW[ CornerSeqSeq[shape.vertex.length] ];

Clear vertex normals

IF NOT preNormaled THEN FOR i: NAT IN [0..shape.shade.length) DO

IF shape.shade[i] # NIL THEN { OPEN shape.shade[i]; [xn, yn, zn] ← nullTriple; };

ENDLOOP;

FOR i: NAT IN [0..shape.numSurfaces) DO IF surface[i] # NIL THEN {

nVtces: NAT ← surface[i].nVtces;

normal: Triple ← nullTriple;

concave: REF BoolSequence ← NEW[ BoolSequence[nVtces] ];

cNmls: REF TripleSequence ← NEW[ TripleSequence[nVtces] ];

Get polygon normal robustly ( allowing slightly concave polygons ). Sum of normals given at corners is assumed to be the dominant direction. Normals over 90 degrees off that are assumed to come from concave vertices and are therefore reversed.

FOR cVtx: NAT IN [0..nVtces) DO -- get normal for each corner

vtx: NAT ← surface[i].vtxPtr[cVtx];

nVtx: NAT ← surface[i].vtxPtr[(cVtx + 1) MOD nVtces];

lVtx: NAT ← surface[i].vtxPtr[(cVtx + nVtces - 1) MOD nVtces];

cNmls[cVtx] ← Cross[ -- in object space so do right-handed

DiffPosns[ shape.vertex[lVtx]^, shape.vertex[vtx]^ ],

DiffPosns[ shape.vertex[nVtx]^, shape.vertex[vtx]^ ]

];

IF unitizeNormals THEN cNmls[cVtx] ← Nmlize[cNmls[cVtx]];

normal ← Add[ normal, cNmls[cVtx] ]; -- sum normals

ENDLOOP;

FOR cVtx: NAT IN [0..nVtces) DO -- Get normals robustly

IF Dot[ cNmls[cVtx], normal ] < 0.0

THEN { -- more than 90 degrees off poly norm.

cNmls[cVtx] ← Negate[ cNmls[cVtx] ];

normal ← Add[ normal, cNmls[cVtx] ]; -- cancel 1st entry

normal ← Add[ normal, cNmls[cVtx] ]; -- contribute to sum

concave[cVtx] ← TRUE; -- put concave tag in here

}

ELSE concave[cVtx] ← FALSE;

ENDLOOP;

FOR cVtx: NAT IN [0..nVtces) DO

vtx: NAT ← surface[i].vtxPtr[cVtx];

IF shape.shade[vtx] # NIL THEN {

OPEN shape.shade[vtx];

IF preNormaled

THEN cNmls[cVtx] ← [xn, yn, zn] -- Get predefined normal

ELSE [[xn, yn, zn]] ← Add[[xn, yn, zn], cNmls[cVtx]]; -- sum normals

};

ENDLOOP;

Build corner structure

FOR cVtx: NAT IN [0..nVtces) DO -- get direction vectors for each edge at vtx.

vtx: NAT ← surface[i].vtxPtr[cVtx];

nVtx: NAT ← surface[i].vtxPtr[(cVtx + 1) MOD nVtces];

lVtx: NAT ← surface[i].vtxPtr[(cVtx + nVtces - 1) MOD nVtces];

corners[vtx] ← UpdateCornerVecSeq[

corners[vtx],

[ lVtx, nVtx, -- store number of incoming vertex and outgoing vertex

DiffPosns[shape.vertex[lVtx]^, shape.vertex[vtx]^], -- direction to incoming vertex

DiffPosns[shape.vertex[nVtx]^, shape.vertex[vtx]^], -- outgoing direction

cNmls[cVtx], -- normal at corner

nullTriple, -- interior knot

concave[cVtx] -- concave tag

]

];

ENDLOOP;

};

ENDLOOP;

corners.length ← shape.vertex.length;

FOR i: NAT IN [0..shape.shade.length) DO -- normalize new vertex normals, store in corners

IF shape.shade[i] # NIL THEN {

OPEN shape.shade[i];

IF Length[ [xn, yn, zn] ] > shape.boundingRadius * .0001

THEN [[xn, yn, zn]] ← Nmlize[ [xn, yn, zn] ]

ELSE [xn, yn, zn] ← nullTriple; -- likely unused, set default to stop trouble

IF corners[i] # NIL THEN FOR j: NAT IN [0..corners[i].length) DO

corners[i][j].normal ← [xn, yn, zn];

ENDLOOP;

};

ENDLOOP;

RETURN[ corners ];

};

UpdateCornerVecSeq: PROC[corner: REF CornerSeq, entry: Corner]
RETURNS[REF CornerSeq] ~ {

newSeq: REF CornerSeq;

IF corner = NIL

THEN newSeq ← NEW[ CornerSeq[6] ] -- get brand new sequence

ELSE IF corner.length = corner.maxLength

THEN { -- expand filled sequence

newSeq ← NEW[ CornerSeq[ corner.maxLength * 2 ] ];

FOR i: NAT IN [0..corner.maxLength) DO

newSeq[i] ← corner[i]; -- copy into new sequence

ENDLOOP;

}

ELSE newSeq ← corner; -- no changes required

corner ← newSeq;

corner[corner.length] ← entry;

corner.length ← corner.length + 1;

RETURN[corner];

};

FindContinuousEdges: PROC[ shape: REF ShapeInstance, vtx: NAT, corner: REF CornerSeq ]
RETURNS[ REF CornerSeq ] ~ {

Make tangents continuous if within 30 degrees of being so. Always make continuous if open edge, adjacent edges not allowed to be

nCorners: NAT ← corner.length;

acrossFrom: REF NatSequenceSequence ← NEW[NatSequenceSequence[nCorners]];

FOR this: NAT IN [0..nCorners) DO

acrossFrom[this] ← NEW[NatSequence[nCorners]];

ENDLOOP;

Check for open edge, if there, align tangents unless included angle less than 45 degrees

IF corner[nCorners-1].inVtx # corner[0].outVtx

THEN { -- open edge (should only be one)

cosAng: REAL ← Dot[Nmlize[corner[nCorners-1].inDir], Nmlize[ corner[0].outDir]];

IF cosAng < minCosToAlignOpen THEN { -- included angle over limit (aligned => -1.0)

IF unitizeNormals THEN { -- normalize to give equal weight to direction

corner[nCorners-1].inDir ← Nmlize[corner[nCorners-1].inDir];

corner[0].outDir ← Nmlize[corner[0].outDir];

};

corner[nCorners-1].inDir ← Add[ -- sum to get aligned direction

corner[nCorners-1].inDir, Negate[corner[0].outDir]

];

corner[0].outDir ← Negate[corner[nCorners-1].inDir]; -- opposite dir

corner[nCorners-1].inDir ← ScaleTangent[ -- scale inDir to Bezier length

corner[nCorners-1].inDir, -- outdir done below

DiffPosns[shape.vertex[corner[nCorners-1].inVtx]^, shape.vertex[vtx]^]

];

};

}

ELSE SELECT nCorners FROM -- no open edge

1, 2 => SIGNAL ThreeDBasics.Error[[$MisMatch, "too few edges at vertex"]];

3 => {}; -- leave things alone if 3

4 => FOR i: NAT IN [0..2) DO -- align opposing vertices if 4

o: NAT ← i+2; o1: NAT ← i+1; i1: NAT ← (i+3) MOD 4; -- opposite, next, and prev.

corner[o].outDir ← corner[o1].inDir ← Add[ -- sum for aligned dir

corner[o].outDir, Negate[corner[i].outDir]

];

corner[i].outDir ← corner[i1].inDir ← Negate[corner[o].outDir];

ENDLOOP;

ENDCASE => {

};

This will attempt to align edges in the more complex cases

IF nCorners > 50 THEN { -- for corners over 4

FOR this: NAT IN [0..nCorners) DO -- tag nearly continuous pairs

FOR other: NAT IN (this+1..nCorners) DO -- don't test adjacent edges, musn't be aligned

cosAng: REAL ← Dot[Nmlize[corner[other].outDir], Nmlize[corner[this].outDir]];

IF this = 0 AND other = nCorners-1 AND corner[other].inVtx = corner[this].outVtx

THEN EXIT; -- skip if adjacent edge wrapping around zero

IF cosAng < minCosToAlign THEN { -- included angle over limit, mark both edges

acrossFrom[this][acrossFrom[this].length] ← other;

acrossFrom[this].length ← acrossFrom[this].length + 1;

acrossFrom[other][acrossFrom[other].length] ← this;

acrossFrom[other].length ← acrossFrom[other].length + 1;

};

ENDLOOP;

FOR i: NAT IN [0..nCorners) DO -- align paired tangents

Sum: PROC[ k: NAT ] ~ {

FOR j: NAT IN [1..acrossFrom[k].length) DO -- sum tangents across from this one

corner[acrossFrom[k][0]].outDir ← Add[

corner[acrossFrom[k][0]].outDir, corner[acrossFrom[k][j]].outDir

];

ENDLOOP;

};

Copy: PROC[ k: NAT ] ~ {

FOR j: NAT IN [1..acrossFrom[k].length) DO -- copy sum to other tangents

corner[acrossFrom[k][j]].outDir ← corner[acrossFrom[k][0]].outDir;

ENDLOOP;

};

Kill: PROC[ k, other: NAT ] ~ {

FOR j: NAT IN [1..acrossFrom[k].length) DO -- kill pointers to prevent further use

IF j # other THEN acrossFrom[acrossFrom[k][j]].length ← 0;

ENDLOOP;

acrossFrom[k].length ← 0;

};

this, last, bigOne: NAT ← i;

biggest: BOOLEAN ← FALSE;

WHILE NOT biggest DO -- chain through to largest set of paired tangents

biggestFound: NAT ← acrossFrom[this].length;

biggest ← TRUE; bigOne ← this;

FOR j: NAT IN [0..acrossFrom[this].length) DO -- check all edges paired with this one

IF acrossFrom[acrossFrom[this][j]].length >= biggestFound THEN {

bigOne ← acrossFrom[this][j]; -- found one the same size at least

IF acrossFrom[acrossFrom[this][j]].length > biggestFound THEN {-- a bigger one

biggestFound ← acrossFrom[acrossFrom[this][j]].length; biggest ← FALSE;

};

ENDLOOP;

last ← this; this ← bigOne;

ENDLOOP;

IF acrossFrom[bigOne].length > 1 AND acrossFrom[last].length > 1 THEN {

FOR j: NAT IN [0..acrossFrom[bigOne].length) DO -- cull any neighboring edges

IF (acrossFrom[bigOne][j] = (last + 1) MOD nCorners)
OR (acrossFrom[bigOne][j] = (last + nCorners-1) MOD nCorners)

THEN {

FOR k: NAT IN [j..acrossFrom[bigOne].length) DO

acrossFrom[bigOne][k] ← acrossFrom[bigOne][k+1];

ENDLOOP;

acrossFrom[bigOne].length ← acrossFrom[bigOne].length - 1;

};

ENDLOOP;

};

Sum[bigOne]; Sum[last]; -- sum all directions in set

IF bigOne # last THEN {

corner[acrossFrom[last][0]].outDir ← Add[

corner[acrossFrom[last][0]].outDir, -- get aligned direction

Negate[corner[acrossFrom[bigOne][0]].outDir]

];

corner[acrossFrom[bigOne][0]].outDir ← Negate[ corner[acrossFrom[last][0]].outDir ];

};

Copy[bigOne]; Copy[last]; -- copy directions to others in sets

Kill[bigOne, last]; Kill[last, bigOne]; -- kill sets

ENDLOOP;

};

FOR this: NAT IN [0..nCorners) DO -- go back over tangents and scale properly

last: NAT ← (this + nCorners -1) MOD nCorners;

corner[this].outDir ← ScaleTangent[

corner[this].outDir,

DiffPosns[shape.vertex[corner[this].outVtx]^, shape.vertex[vtx]^]

];

IF corner[last].inVtx = corner[this].outVtx THEN corner[last].inDir ← corner[this].outDir;

ENDLOOP;

RETURN[ corner ];

};

SortVertex: PROC[corner: REF CornerSeq] RETURNS[REF CornerSeq] ~ {

Sort polygon entries to clockwise order at each vertex, ensure discontinuities are at extremes

Build chain of corners by checking both ends of chain against all remaining unattached corners, only one chain allowed, since only one open edge allowed at vertex

nCrnrs: NAT ← corner.length;

someLeft, someFound: BOOLEAN ← TRUE;

newSeq: REF CornerSeq ← NEW[CornerSeq[nCrnrs]];

newSeq[0] ← corner[0]; newSeq.length ← 1;

WHILE someLeft DO

someLeft ← someFound ← FALSE;

FOR j: NAT IN [1..nCrnrs) DO

IF newSeq[newSeq.length-1].inVtx = corner[j].outVtx -- match last incoming edge

THEN { -- next corner in clockwiser order

newSeq[newSeq.length] ← corner[j]; newSeq.length ← newSeq.length+1;

corner[j].outVtx ← corner[j].inVtx ← LAST[NAT]; -- no further use

someFound ← TRUE;

}

ELSE IF newSeq[0].outVtx = corner[j].inVtx -- match 1st outgoing edge

THEN { -- previous corner in clockwiser order

FOR k: NAT DECREASING IN [0..newSeq.length) DO

newSeq[k+1] ← newSeq[k];

ENDLOOP;

newSeq[0] ← corner[j]; newSeq.length ← newSeq.length+1;

corner[j].outVtx ← corner[j].inVtx ← LAST[NAT]; -- no further use

someFound ← TRUE;

}

ELSE IF corner[j].outVtx # LAST[NAT] THEN someLeft ← TRUE; -- not done

ENDLOOP;

IF NOT someFound AND someLeft THEN -- more than one chain, apparently

SIGNAL ThreeDBasics.Error[[$Fatal, "Multiple open edges at a vertex not allowed"]];

ENDLOOP;

IF newSeq.length > 0 THEN corner ← newSeq;

RETURN[ corner ];

};

InitClasses[];

END.