[Cyan]<CedarChest6.0>SolidModeler>SVMappings.mesa!1

SVMappings.mesa

Last Edited by Bier on December 19, 1982 2:04 am

Author: Eric Bier on July 31, 1985 11:41:12 pm PDT
Contents: A set of bidirectional mappings between 3d surfaces and a 2d image plane

DIRECTORY

Imager,

Rope,

SV2d,

SV3d,

SVModelTypes;

SVMappings: DEFINITIONS =

BEGIN

Artwork: TYPE = SVModelTypes.Artwork;

Point2d: TYPE = SV2d.Point2d;

Point3d: TYPE = SV3d.Point3d;

Polygon: TYPE = SV2d.Polygon;

Vector: TYPE = SV3d.Vector;

PRect: TYPE = SVModelTypes.PRect;

PDisk: TYPE = SVModelTypes.PDisk;

Tube: TYPE = SVModelTypes.Tube;

Disk: TYPE = SVModelTypes.Disk;

Box: TYPE = SVModelTypes.Box;

TubeLine: TYPE = SVModelTypes.TubeLine;

SpaceFunction: TYPE = SVModelTypes.SpaceFunction;

When you map a straight line in image space onto the surface of a cylinder, you are taking an equation of the form cy -sx -d = 0 and applying the transform:
(x,y) <==> (R*theta, h) giving an equation of the form:
c*h - s*R*theta -d = 0. which is of the same form. Given two points on the cylinder surface, we can find the line that goes through them in a normal fashion and can map this back to the plane by either mapping the endpoints or converting the equation.

CartesianToPolar: PROC [x, y: REAL] RETURNS [r, theta: REAL];

PolarToCartesian: PROC [r, theta: REAL] RETURNS [x, y: REAL];

CreatePDisk: PROC [r: REAL, origin: Point2d] RETURNS [pdisk: PDisk];

DrawPDisk: PROC [dc: Imager.Context, pdisk: PDisk];

The Space Function Simple "Surface"

CreateFunction: PROC [scalars: Point3d] RETURNS [sf: SpaceFunction];

Point3dToFunctionPoint: PROC [point3d: Point3d] RETURNS [sfPoint: Point3d];

FunctionPointToPoint3d: PROC [sfPoint: Point3d, assembly: REF ANY] RETURNS [point3d: Point3d];

The Tube Simple Surface

CreateTube: PROC [R: REAL, H: REAL] RETURNS [tube: Tube];

Point3dToTubePoint: PROC [point3d: Point3d] RETURNS [tubePoint: Point2d];

TubePointToPoint3d: PROC [tubePoint: Point2d, assembly: REF ANY] RETURNS [point3d: Point3d];

ImageToTube: PROC [imagePoint: Point2d, data: REF ANY] RETURNS [surfacePoint: Point2d, onSurf: BOOL];

data will be a Tube. It is a ref any so we can use this mapping in ImagePolyToSurfacePoly below. surfacePoint is a [theta, h] pair.

TubeToImage: PROC [surfacePoint: Point2d, data: REF ANY] RETURNS [imagePoint: Point2d, onSurf: BOOL];

data will be a Tube. It is a ref any so we can use this mapping in SurfacePolyToImagePoly below. surfacePoint is a [theta, h] pair.

The Cylinder Simple Surface

Point3dToDiskPoint: PROC [point3d: Point3d] RETURNS [r, theta: REAL];

DiskPointToPoint3d: PROC [r, theta: REAL, assembly: REF ANY] RETURNS [point3d: Point3d];

ImageToTopDisk: PROC [u,v: REAL, disk: Disk] RETURNS [r, theta: REAL];

TopDiskToImage: PROC [r, theta: REAL, disk: Disk] RETURNS [u,v: REAL];

ImageDiskToTopDiskBoundary: PROC [pdisk: PDisk, disk: Disk] RETURNS [R, halfH: REAL];

TopDiskBoundaryToImageDisk: PROC [R, halfH: REAL, disk: Disk] RETURNS [pdisk: PDisk];

ImageToBottomDisk: PROC [u,v: REAL, disk: Disk] RETURNS [r, theta: REAL];

BottomDiskToImage: PROC [r, theta: REAL, disk: Disk] RETURNS [u,v: REAL];

ImageDiskToBottomDiskBoundary: PROC [pdisk: PDisk, disk: Disk] RETURNS [R, halfH: REAL];

BottomDiskBoundaryToImageDisk: PROC [R, halfH: REAL, disk: Disk]

RETURNS [pdisk: PDisk];

The Box Simple Surface

Box Mapping
Imagine an unfolded box as follows:
There are four rectangles numbered left to right as 1..4.
Two more rectangles numbered 5 and 6 are above and below rectangle 2 respectively.
Rectangle 2 maps to the front (pos z) side of the box. Square 6 maps to the bottom (neg y) side. All other rectangles map accordingly.
An [x,y] pair maps to a surface point as follows:
If a box has height sy, width sx, and depth sz then the correspondences are:
IF -sy/2 <= y <= sy/2 AND
-(sz+sx) <= x < -sx THEN Rectangle 1.
-sx <= x <= 0 THEN Rectangle 2.
0 < x <= sz THEN Rectangle 3.
sz < x <= sz + sx THEN Rectangle 4.
IF -(sy/2+sz) < y < -sy/2 AND -sx <= x <= 0 THEN Rectangle 6.
IF sy/2 < y < sy/2 + sz AND -sx <= x <= 0 THEN Rectangle 5.
Otherwise, out of box.

CreateBox: PROC [x, y, z: REAL] RETURNS [box: Box];

BoxOrthogonalOInverse: PROC [point3d: Point3d, normal: Vector, box: Box] RETURNS [boxPoint: Point2d, hit: BOOL];

BoxOrthogonalO: PROC [boxPoint: Point2d, box: Box] RETURNS [point3d: Point3d, hit: BOOL];

BoxRadialOInverse: PROC [point3d: Point3d, normal: Vector, box: Box] RETURNS [boxPoint: Point2d, hit: BOOL];

BoxRadialO: PROC [boxPoint: Point2d, box: Box] RETURNS [point3d: Point3d, hit: BOOL];

ImageToBox: PROC [imagePoint: Point2d, data: REF ANY] RETURNS [surfacePoint: Point2d, onSurf: BOOL];

data will be a Box. It is a ref any so we can use this mapping in ImagePolyToSurfacePoly below. surfacePoint is a [x, y] pair (See comment on Box Mapping above).

BoxToImage: PROC [surfacePoint: Point2d, data: REF ANY] RETURNS [imagePoint: Point2d, onSurf: BOOL];

data will be a Box. It is a ref any so we can use this mapping in SurfacePolyToImagePoly below. surfacePoint is a [x, y] pair (See comment on Box Mapping above).

2d Surface Projections

ImagePolyToSurfacePoly: PROC [imagePoly: Polygon, map: PROC [imagePoint: Point2d, data: REF ANY] RETURNS [surfacePoint: Point2d, onSurf: BOOL], data: REF ANY] RETURNS [surfacePoly: Polygon];

data will probably be a REF <Surface> for some type of 3d surface.

SurfacePolyToImagePoly: PROC [surfacePoly: Polygon, map: PROC [surfacePoint: Point2d, data: REF ANY] RETURNS [imagePoint: Point2d, onSurf: BOOL], data: REF ANY] RETURNS [imagePoly: Polygon];

data will probably be a REF <Surface> for some type of 3d surface.

END.