DIRECTORY G3dBasic, G3dPlane, G3dTriangle, G3dVector, Real, RealFns, Rope, ImplicitCubeTet; ImplicitCubeTetImpl: CEDAR MONITOR IMPORTS G3dPlane, G3dTriangle, G3dVector, Real, RealFns EXPORTS ImplicitCubeTet ~ BEGIN Triple: TYPE ~ G3dBasic.Triple; Plane: TYPE ~ G3dPlane.Plane; IntTriple: TYPE ~ G3dTriangle.IntTriple; Segment: TYPE ~ G3dTriangle.Segment; Segments: TYPE ~ G3dTriangle.Segments; Triangle: TYPE ~ G3dTriangle.Triangle; Triangles: TYPE ~ G3dTriangle.Triangles; ROPE: TYPE ~ Rope.ROPE; Cube: TYPE ~ ImplicitCubeTet.Cube; Corner: TYPE ~ ImplicitCubeTet.Corner; EventType: TYPE ~ ImplicitCubeTet.EventType; Event: TYPE ~ ImplicitCubeTet.Event; Events: TYPE ~ ImplicitCubeTet.Events; TetEdge: TYPE ~ ImplicitCubeTet.TetEdge; TetFace: TYPE ~ ImplicitCubeTet.TetFace; TetIntersection: TYPE ~ ImplicitCubeTet.TetIntersection; TetIntersections: TYPE ~ ImplicitCubeTet.TetIntersections; TetIntersectProc: TYPE ~ ImplicitCubeTet.TetIntersectProc; TetProc: TYPE ~ ImplicitCubeTet.TetProc; Tetrahedron: TYPE ~ ImplicitCubeTet.Tetrahedron; ThreeEdges: TYPE ~ ImplicitCubeTet.ThreeEdges; ThreeCorners: TYPE ~ ImplicitCubeTet.ThreeCorners; TwoCorners: TYPE ~ ImplicitCubeTet.TwoCorners; sqRt3: REAL RealFns.SqRt[3.0]; MidCorner: PUBLIC PROC [c1, c2: REF Corner] RETURNS [p: Triple] ~ { p.x IF c1.id.i # c2.id.i THEN 0.5*(c1.pos.x+c2.pos.x) ELSE c1.pos.x; p.y IF c1.id.j # c2.id.j THEN 0.5*(c1.pos.y+c2.pos.y) ELSE c1.pos.y; p.z IF c1.id.k # c2.id.k THEN 0.5*(c1.pos.z+c2.pos.z) ELSE c1.pos.z; }; InterpCorners: PUBLIC PROC [t: REAL, c1, c2: REF Corner] RETURNS [p: Triple] ~ { p.x IF c1.id.i # c2.id.i THEN c1.pos.x+t*(c2.pos.x-c1.pos.x) ELSE c1.pos.x; p.y IF c1.id.j # c2.id.j THEN c1.pos.y+t*(c2.pos.y-c1.pos.y) ELSE c1.pos.y; p.z IF c1.id.k # c2.id.k THEN c1.pos.z+t*(c2.pos.z-c1.pos.z) ELSE c1.pos.z; }; IntersectWithSurface: PUBLIC PROC [tet: REF Tetrahedron, action: TetIntersectProc] ~ { Pos: PROC [c: REF Corner, i: INT] RETURNS [j: INT] ~ {j IF c.state = positive THEN i ELSE 0}; SELECT (Pos[tet.a, 8]+Pos[tet.b, 4]+Pos[tet.c, 2]+Pos[tet.d, 1]) FROM 1 => action[3, bd, cd, ad, ab]; 2 => action[3, ac, cd, bc, ab]; 3 => action[4, ad, bd, bc, ac]; 4 => action[3, ab, bc, bd, ab]; 5 => action[4, ad, ab, bc, cd]; 6 => action[4, ab, ac, cd, bd]; 7 => action[3, ab, ac, ad, ab]; 8 => action[3, ab, ad, ac, ab]; 9 => action[4, ab, bd, cd, ac]; 10 => action[4, ab, ad, cd, bc]; 11 => action[3, ab, bd, bc, ab]; 12 => action[4, ad, ac, bc, bd]; 13 => action[3, cd, ac, bc, ab]; 14 => action[3, bd, ad, cd, ab]; ENDCASE; -- 0, 15 }; FaceName: PUBLIC PROC [f: TetFace] RETURNS [r: ROPE] ~ { r SELECT f FROM abc=>"abc", abd=>"abd", acd=>"acd", ENDCASE=>"bcd"; }; EdgeName: PUBLIC PROC [e: TetEdge] RETURNS [r: ROPE] ~ { r SELECT e FROM ab=>"ab",ac=>"ac",ad=>"ad",bc=>"bc",bd=>"bd",ENDCASE=>"cd"; }; CornerName: PUBLIC PROC [c: REF Corner, tet: REF Tetrahedron] RETURNS [r: ROPE] ~ { r SELECT c FROM tet.a => "a", tet.b => "b", tet.c => "c", tet.d => "d", ENDCASE => "?"; }; MakeTetrahedron: PUBLIC PROC [ a, b, c, d: REF Corner, which: INT, scratch: REF Tetrahedron NIL] RETURNS [tet: REF Tetrahedron] ~ { IF (tet scratch) = NIL THEN tet NEW[Tetrahedron]; tet.which which; tet.a a; tet.b b; tet.c c; tet.d d; tet.triangles[abc] G3dTriangle.MakeTriangle[a.pos, c.pos, b.pos, tet.triangles[abc]]; tet.triangles[abd] G3dTriangle.MakeTriangle[a.pos, b.pos, d.pos, tet.triangles[abd]]; tet.triangles[acd] G3dTriangle.MakeTriangle[a.pos, d.pos, c.pos, tet.triangles[acd]]; tet.triangles[bcd] G3dTriangle.MakeTriangle[b.pos, c.pos, d.pos, tet.triangles[bcd]]; }; TrianglesInTetrahedron: PUBLIC PROC [ candidates: REF Triangles, tet: REF Tetrahedron, scratch: REF Triangles] RETURNS [ret: REF Triangles] ~ { IF (ret scratch) # NIL THEN ret.length 0; FOR i: INT IN [0..candidates.length) DO t: REF Triangle candidates[i]; IF TriangleInTetrahedron[t, tet] THEN ret G3dTriangle.AddTriangle[t, ret]; ENDLOOP; }; TriangleInTetrahedron: PUBLIC PROC [t: REF Triangle, tet: REF Tetrahedron] RETURNS [BOOL] ~ { PlaneInTetrahedron: PROC [p: Plane] RETURNS [b: BOOL] ~ { Pos: PROC [c: REF Corner, type: CornerType] RETURNS [b: BOOL] ~ { d: REAL c.pos.x*p.x+c.pos.y*p.y+c.pos.z*p.z+p.w; cInfo[type] [TRUE, d, b d > 0.0, c]; }; s: BOOL Pos[tet.a, a]; b Pos[tet.b, b] # s OR Pos[tet.c, c] # s OR Pos[tet.d, d] # s; }; CornerInfo: TYPE ~ RECORD [set: BOOL, distance: REAL, pos: BOOL, c: REF Corner]; CornerType: TYPE ~ {a, b, c, d}; cInfo: ARRAY CornerType OF CornerInfo ALL[[FALSE, 0.0, FALSE, NIL]]; IF PlaneInTetrahedron[t.plane] THEN { Code: TYPE ~ ARRAY TetFace OF BOOL; SetCodes: PROC RETURNS [ARRAY [0..3) OF Code] ~ { Set: PROC [t: Triple] RETURNS [r: Code] ~ { FOR face: TetFace IN TetFace DO plane: Plane tet.triangles[face].plane; -- planes point inwards r[face] t.x*plane.x+t.y*plane.y+t.z*plane.z+plane.w < 0.0; ENDLOOP; }; RETURN[[Set[t.p1], Set[t.p2], Set[t.p3]]]; }; NoneSet: PROC [c: Code] RETURNS [b: BOOL TRUE] ~ { FOR face: TetFace IN TetFace DO IF c[face] THEN RETURN[FALSE]; ENDLOOP; }; Cross: PROC [p1, p2: Triple] RETURNS [b: BOOL FALSE] ~ { FOR face: TetFace IN TetFace DO IF G3dTriangle.IntersectTriangle[p1, p2, tet.triangles[face]].intersect THEN RETURN[TRUE]; ENDLOOP; }; SetInfo: PROC [c: REF Corner] RETURNS [i: CornerInfo] ~ { d: REAL c.pos.x*t.plane.x+c.pos.y*t.plane.y+c.pos.z*t.plane.z+t.plane.w; RETURN[[TRUE, d, d > 0.0, c]]; }; Hit: PROC [t1, t2: CornerType] RETURNS [b: BOOL] ~ { c1: CornerInfo cInfo[t1]; c2: CornerInfo cInfo[t2]; a: REAL c1.distance/(c1.distance-c2.distance); b G3dTriangle.InsideTriangle[InterpCorners[a, c1.c, c2.c], t]; }; out: ARRAY [0..3) OF Code SetCodes[]; FOR face: TetFace IN TetFace DO IF out[0][face] AND out[1][face] AND out[2][face] THEN RETURN[FALSE]; ENDLOOP; FOR i: INT IN [0..3) DO IF NoneSet[out[i]] THEN RETURN[TRUE]; ENDLOOP; IF Cross[t.p1, t.p2] OR Cross[t.p2, t.p3] OR Cross[t.p3, t.p1] THEN RETURN[TRUE]; -- ab -- IF cInfo[a].pos # cInfo[b].pos AND Hit[a, b] THEN RETURN[TRUE]; -- ac -- IF NOT cInfo[c].set THEN cInfo[c] SetInfo[tet.c]; IF cInfo[a].pos # cInfo[c].pos AND Hit[a, c] THEN RETURN[TRUE]; -- ad -- IF NOT cInfo[d].set THEN cInfo[d] SetInfo[tet.d]; IF cInfo[a].pos # cInfo[d].pos AND Hit[a, d] THEN RETURN[TRUE]; -- bc -- IF cInfo[b].pos # cInfo[c].pos AND Hit[b, c] THEN RETURN[TRUE]; -- bd -- IF cInfo[b].pos # cInfo[d].pos AND Hit[b, d] THEN RETURN[TRUE]; -- cd -- IF cInfo[c].pos # cInfo[d].pos AND Hit[c, d] THEN RETURN[TRUE]; }; RETURN[FALSE]; }; InsideTetrahedron: PUBLIC PROC [t: REF Tetrahedron, p: Triple] RETURNS [BOOL] ~ { Test: PROC [face: TetFace] RETURNS [BOOL] ~ { RETURN[G3dPlane.Side[p, t.triangles[face].plane] = positive]; }; RETURN[Test[abc] AND Test[abd] AND Test[acd] AND Test[bcd]]; }; EdgesFromFace: PUBLIC PROC [f: TetFace] RETURNS [r: ThreeEdges] ~ { r SELECT f FROM abc => [ab, ac, bc], abd => [ab, ad, bd], acd => [ac, ad, cd], ENDCASE => [bc, bd, cd]; }; CornersFromFace: PUBLIC PROC [f: TetFace, t: REF Tetrahedron] RETURNS [r: ThreeCorners] ~ { r SELECT f FROM abc => [t.a, t.b, t.c], abd => [t.a, t.b, t.d], acd => [t.a, t.c, t.d], ENDCASE => [t.b, t.c, t.d]; }; CornersFromEdge: PUBLIC PROC [e: TetEdge, t: REF Tetrahedron] RETURNS [r: TwoCorners] ~ { r SELECT e FROM ab => [t.a, t.b], ac => [t.a, t.c], ad => [t.a, t.d], bc => [t.b, t.c], bd => [t.b, t.d], ENDCASE => [t.c, t.d]; }; MidEdge: PUBLIC PROC [tet: REF Tetrahedron, e: TetEdge] RETURNS [Triple] ~ { tc: TwoCorners CornersFromEdge[e, tet]; RETURN[MidCorner[tc.a, tc.b]]; }; LRFaces: PUBLIC PROC [e: TetEdge] RETURNS [l, r: TetFace] ~ {RETURN[LFace[e], RFace[e]]}; LFace: PUBLIC PROC [e: TetEdge] RETURNS [f: TetFace] ~ { f SELECT e FROM ab=>abd, ac=>abc, ad=>acd, bc=>bcd, bd=>abd, ENDCASE=>bcd; }; RFace: PUBLIC PROC [e: TetEdge] RETURNS [f: TetFace] ~ { f SELECT e FROM ab=>abc, ac=>acd, ad=>abd, bc=>abc, bd=>bcd, ENDCASE=>acd; }; Decompose: PUBLIC PROC [c: REF Cube, action: TetProc, scratch: REF Tetrahedron NIL] ~ { odd: BOOL (c.id.i+c.id.j+c.id.k) MOD 2 # 0; FOR i: INT IN [0..5) DO IF NOT action[InnerGetTetN[c, odd, i, scratch]] THEN EXIT; ENDLOOP; }; GetTetN: PUBLIC PROC [c: REF Cube, which: INT, scratch: REF Tetrahedron NIL] RETURNS [t: REF Tetrahedron] ~ { t InnerGetTetN[c, (c.id.i+c.id.j+c.id.k) MOD 2 # 0, which, scratch]; }; InnerGetTetN: PROC [cube: REF Cube, odd: BOOL, which: INT, scratch: REF Tetrahedron NIL] RETURNS [tet: REF Tetrahedron] ~ { Inner: PROC [a, b, c, d: REF Corner] ~ { tet MakeTetrahedron[a, b, c, d, which, scratch]; tet.cube cube; }; IF odd THEN SELECT which FROM 0 => Inner[cube.lbn, cube.lbf, cube.ltn, cube.rbn]; 1 => Inner[cube.ltf, cube.ltn, cube.lbf, cube.rtf]; 2 => Inner[cube.rbf, cube.rbn, cube.rtf, cube.lbf]; 3 => Inner[cube.rtn, cube.rtf, cube.rbn, cube.ltn]; 4 => Inner[cube.lbf, cube.ltn, cube.rbn, cube.rtf]; ENDCASE => ERROR ELSE SELECT which FROM 0 => Inner[cube.lbf, cube.rbf, cube.ltf, cube.lbn]; 1 => Inner[cube.ltn, cube.ltf, cube.rtn, cube.lbn]; 2 => Inner[cube.rbn, cube.rbf, cube.lbn, cube.rtn]; 3 => Inner[cube.rtf, cube.rtn, cube.ltf, cube.rbf]; 4 => Inner[cube.lbn, cube.ltf, cube.rtn, cube.rbf]; ENDCASE => ERROR; }; IDFromPoint: PUBLIC PROC [p: Triple, size: REAL, offset: Triple []] RETURNS [id: IntTriple] ~ { id [Real.Round[(p.x-offset.x)/size+0.5], Real.Round[(p.y-offset.y)/size+0.5], Real.Round[(p.z-offset.z)/size+0.5]]; }; PointFromID: PUBLIC PROC [id: IntTriple, size: REAL] RETURNS [p: Triple] ~ { p [id.i*size, id.j*size, id.k*size]; }; NewCube: PROC [id: IntTriple, size: REAL, offset: Triple [], scratch: REF Cube NIL] RETURNS [c: REF Cube] ~ { c IF scratch # NIL THEN scratch ELSE NEW[Cube]; c.id id; c.diag size*sqRt3; c.l offset.x+(REAL[id.i]-0.5)*size; c.r c.l+size; c.b offset.y+(REAL[id.j]-0.5)*size; c.t c.b+size; c.n offset.z+(REAL[id.k]-0.5)*size; c.f c.n+size; }; SetCube: PUBLIC PROC [ id: IntTriple, lbn, lbf, ltn, ltf, rbn, rbf, rtn, rtf: REF Corner, offset: Triple [], scratch: REF Cube NIL] RETURNS [c: REF Cube] ~ { c NewCube[id, rbn.pos.x-lbn.pos.x, offset, scratch]; c.lbn lbn; c.lbf lbf; c.ltn ltn; c.ltf ltf; c.rbn rbn; c.rbf rbf; c.rtn rtn; c.rtf rtf; }; MakeCube: PUBLIC PROC [id: IntTriple, size: REAL, offset: Triple [], scratch: REF Cube NIL] RETURNS [c: REF Cube] ~ { Set: PROC [x, y, z: REAL, i, j, k: INT] RETURNS [c: REF Corner] ~ { c NEW[Corner [[i, j, k], [x, y, z], 0, unset, FALSE]]; }; c NewCube[id, size, offset, scratch]; c.lbn Set[c.l, c.b, c.n, id.i, id.j, id.k]; c.lbf Set[c.l, c.b, c.f, id.i, id.j, id.k+1]; c.ltn Set[c.l, c.t, c.n, id.i, id.j+1, id.k]; c.ltf Set[c.l, c.t, c.f, id.i, id.j+1, id.k+1]; c.rbn Set[c.r, c.b, c.n, id.i+1, id.j, id.k]; c.rbf Set[c.r, c.b, c.f, id.i+1, id.j, id.k+1]; c.rtn Set[c.r, c.t, c.n, id.i+1, id.j+1, id.k]; c.rtf Set[c.r, c.t, c.f, id.i+1, id.j+1, id.k+1]; }; TriangleInCube: PUBLIC PROC [t: REF Triangle, c: REF Cube] RETURNS [BOOL] ~ { PlaneInCube: PROC [p: Plane] RETURNS [in: BOOL] ~ { Pos: PROC [c: REF Corner, type: CornerType] RETURNS [b: BOOL] ~ { d: REAL c.pos.x*p.x+c.pos.y*p.y+c.pos.z*p.z+p.w; cInfo[type] [TRUE, d, b d > 0.0, c]; }; s: BOOL Pos[c.lbn, lbn]; in IF ABS[cInfo[lbn].distance] > c.diag THEN FALSE ELSE Pos[c.lbf, lbf] # s OR Pos[c.ltn, ltn] # s OR Pos[c.ltf, ltf] # s OR Pos[c.rbn, rbn] # s OR Pos[c.rbf, rbf] # s OR Pos[c.rtn, rtn] # s OR Pos[c.rtf, rtf] # s; }; CornerInfo: TYPE ~ RECORD [set: BOOL, distance: REAL, pos: BOOL, c: REF Corner]; CornerType: TYPE ~ {lbn, lbf, ltn, ltf, rbn, rbf, rtn, rtf}; cInfo: ARRAY CornerType OF CornerInfo ALL[[FALSE, 0.0, FALSE, NIL]]; IF PlaneInCube[t.plane] THEN { Face: TYPE ~ {l, r, b, t, n, f}; Code: TYPE ~ ARRAY Face OF BOOL; SetCodes: PROC RETURNS [ARRAY [0..3) OF Code] ~ { Set: PROC [t: Triple] RETURNS [r: Code] ~ {r[t.xc.r,t.yc.t,t.zc.f]}; RETURN[[Set[t.p1], Set[t.p2], Set[t.p3]]]; }; NoneSet: PROC [c: Code] RETURNS [b: BOOL TRUE] ~ { FOR face: Face IN Face DO IF c[face] THEN RETURN[FALSE]; ENDLOOP; }; SetInfo: PROC [c: REF Corner] RETURNS [i: CornerInfo] ~ { d: REAL c.pos.x*t.plane.x+c.pos.y*t.plane.y+c.pos.z*t.plane.z+t.plane.w; RETURN[[TRUE, d, d > 0.0, c]]; }; Hit: PROC [t1, t2: CornerType] RETURNS [b: BOOL] ~ { c1: CornerInfo cInfo[t1]; c2: CornerInfo cInfo[t2]; a: REAL c1.distance/(c1.distance-c2.distance); b G3dTriangle.InsideTriangle[InterpCorners[a, c1.c, c2.c], t]; }; out: ARRAY [0..3) OF Code SetCodes[]; FOR face: Face IN Face DO IF out[0][face] AND out[1][face] AND out[2][face] THEN RETURN[FALSE]; ENDLOOP; FOR i: INT IN [0..3) DO IF NoneSet[out[i]] THEN RETURN[TRUE]; ENDLOOP; FOR i: INT IN [0..3) DO Cross: PROC [face: Face, e, e1, e2, a1, a2, amn, amx, b1, b2, bmn, bmx: REAL] RETURNS [b: BOOL FALSE] ~ { IF out[i][face] # out[j][face] THEN { a: REAL (e-e1)/(e2-e1); IF amn > amx OR bmn > bmx THEN ERROR; b (a1+a*(a2-a1)) IN [amn..amx] AND (b1+a*(b2-b1)) IN [bmn..bmx]; }; }; p, q: Triple; j: INT (i+1) MOD 3; SELECT i FROM 0 => {p t.p1; q t.p2}; 1 => {p t.p2; q t.p3}; ENDCASE => {p t.p3; q t.p1}; IF Cross[l, c.l, p.x, q.x, p.y, q.y, c.b, c.t, p.z, q.z, c.n, c.f] OR Cross[r, c.r, p.x, q.x, p.y, q.y, c.b, c.t, p.z, q.z, c.n, c.f] OR Cross[b, c.b, p.y, q.y, p.x, q.x, c.l, c.r, p.z, q.z, c.n, c.f] OR Cross[t, c.t, p.y, q.y, p.x, q.x, c.l, c.r, p.z, q.z, c.n, c.f] OR Cross[n, c.n, p.z, q.z, p.x, q.x, c.l, c.r, p.y, q.y, c.b, c.t] OR Cross[f, c.f, p.z, q.z, p.x, q.x, c.l, c.r, p.y, q.y, c.b, c.t] THEN RETURN[TRUE]; ENDLOOP; -- lb -- IF cInfo[lbn].pos # cInfo[lbf].pos AND Hit[lbn, lbf] THEN RETURN[TRUE]; -- ln -- IF NOT cInfo[ltn].set THEN cInfo[ltn] SetInfo[c.ltn]; IF cInfo[lbn].pos # cInfo[ltn].pos AND Hit[lbn, ltn] THEN RETURN[TRUE]; -- lt -- IF NOT cInfo[ltf].set THEN cInfo[ltf] SetInfo[c.ltf]; IF cInfo[ltn].pos # cInfo[ltf].pos AND Hit[ltn, ltf] THEN RETURN[TRUE]; -- lf -- IF cInfo[ltf].pos # cInfo[lbf].pos AND Hit[ltf, lbf] THEN RETURN[TRUE]; -- rb -- IF NOT cInfo[rbn].set THEN cInfo[rbn] SetInfo[c.rbn]; IF NOT cInfo[rbf].set THEN cInfo[rbf] SetInfo[c.rbf]; IF cInfo[rbn].pos # cInfo[rbf].pos AND Hit[rbn, rbf] THEN RETURN[TRUE]; -- rf -- IF NOT cInfo[rtf].set THEN cInfo[rtf] SetInfo[c.rtf]; IF cInfo[rtf].pos # cInfo[rbf].pos AND Hit[rtf, rbf] THEN RETURN[TRUE]; -- rt -- IF NOT cInfo[rtn].set THEN cInfo[rtn] SetInfo[c.rtn]; IF cInfo[rtn].pos # cInfo[rtf].pos AND Hit[rtn, rtf] THEN RETURN[TRUE]; -- rn -- IF cInfo[rtn].pos # cInfo[rbn].pos AND Hit[rtn, rbn] THEN RETURN[TRUE]; -- bn -- IF cInfo[lbn].pos # cInfo[rbn].pos AND Hit[lbn, rbn] THEN RETURN[TRUE]; -- bf -- IF cInfo[lbf].pos # cInfo[rbf].pos AND Hit[lbf, rbf] THEN RETURN[TRUE]; -- tn -- IF cInfo[ltn].pos # cInfo[rtn].pos AND Hit[ltn, rtn] THEN RETURN[TRUE]; -- tf -- IF cInfo[ltf].pos # cInfo[rtf].pos AND Hit[ltf, rtf] THEN RETURN[TRUE]; }; RETURN[FALSE]; }; TrianglesInCube: PUBLIC PROC [ candidates: REF Triangles, cube: REF Cube, scratch: REF Triangles NIL] RETURNS [ret: REF Triangles] ~ { IF (ret scratch) # NIL THEN ret.length 0; FOR i: INT IN [0..candidates.length) DO t: REF Triangle candidates[i]; IF TriangleInCube[t, cube] THEN ret G3dTriangle.AddTriangle[t, ret]; ENDLOOP; }; Side: TYPE ~ {in, on, out}; EndState: TYPE ~ RECORD [side: Side, face: TetFace]; EventName: PUBLIC PROC [e: Event] RETURNS [r: Rope.ROPE] ~ { r SELECT e.type FROM entry=> "entry", exit=> "exit", inside=> "inside", ENDCASE=> "graze"; }; scratchEvents: ARRAY [0..10) OF REF Events ALL[NIL]; ObtainEvents: ENTRY PROC RETURNS [REF Events] ~ { FOR i: INT IN [0..10) DO s: REF Events scratchEvents[i]; IF s # NIL THEN {scratchEvents[i] NIL; s.length 0; RETURN[s]}; ENDLOOP; RETURN[NEW[Events[12]]]; }; ReleaseEvents: ENTRY PROC [scratch: REF Events] ~ { FOR i: INT IN [0..10) DO IF scratchEvents[i] = NIL THEN {scratchEvents[i] scratch; EXIT}; ENDLOOP; }; AddEvent: PROC [e: Event, events: REF Events] RETURNS [r: REF Events] ~ { LengthenEvents: PROC [events: REF Events] RETURNS [new: REF Events] ~ { newLength: NAT MAX[Real.Ceiling[1.3*events.maxLength], 3]; new NEW[Events[newLength]]; FOR i: NAT IN [0..events.length) DO new[i] events[i]; ENDLOOP; new.length events.length; }; IF (r events) = NIL THEN r NEW[Events[1]]; IF r.length = r.maxLength THEN r LengthenEvents[r]; r[r.length] e; r.length r.length+1; }; GetEvents: PUBLIC PROC [ tet: REF Tetrahedron, segments: REF Segments, epsilon: REAL, insideToo: BOOL, scratch: REF Events NIL] RETURNS [events: REF Events] ~ { Info: TYPE ~ RECORD [nInts: INT, p1, p2: Triple, f1, f2: TetFace]; GetEndState: PROC [p: Triple] RETURNS [s: EndState [in, abc]] ~ { near: BOOL FALSE; nearFace: TetFace; FOR l: LIST OF TetFace LIST[abc, abd, acd, bcd], l.rest WHILE l # NIL DO d: REAL G3dPlane.DistanceToPoint[p, tet.triangles[l.first].plane, FALSE]; IF d < -epsilon THEN RETURN[[out, abc]]; IF ABS[d] < epsilon THEN {near TRUE; nearFace l.first}; ENDLOOP; RETURN[IF near THEN [on, nearFace] ELSE [in, abc]]; }; end1: EndState GetEndState[segments[0].p1]; IF (events scratch) # NIL THEN events.length 0; FOR s: INT IN [0..segments.length) DO Eq: PROC [p, q: Triple] RETURNS [b: BOOL] ~ {b G3dVector.Distance[p, q] < epsilon}; Add: PROC [type: EventType, p: Triple, face: TetFace abc] ~ { e: Event [p, type, face, s]; IF events # NIL AND events.length > 0 AND Eq[p, events[events.length-1].p] THEN {IF events[events.length-1].type = inside THEN events[events.length-1] e} ELSE events AddEvent[e, events]; }; GetInfo: PROC RETURNS [i: Info] ~ { GetAlpha: PROC [f: TetFace] ~ { t: REF Triangle tet.triangles[f]; d1: REAL G3dPlane.DistanceToPoint[seg.p1, t.plane]; d2: REAL G3dPlane.DistanceToPoint[seg.p2, t.plane]; IF (d1 > 0.0) # (d2 > 0.0) THEN { p: Triple G3dVector.Interp[a2 d1/(d1-d2), seg.p1, seg.p2]; IF NOT G3dTriangle.InsideTriangle[p, t] THEN RETURN; IF (i.nInts i.nInts+1) = 1 THEN {a1 a2; i.p1 p; i.f1 f} ELSE IF a2 < a1 THEN {i.p2 i.p1; i.f2 i.f1; i.p1 p; i.f1 f} ELSE {i.p2 p; i.f2 f}; IF i.nInts = 2 AND (end1.side # out OR end2.side # out) THEN i.nInts 1; }; }; a1, a2: REAL; FOR f: TetFace IN TetFace DO IF i.nInts = 2 THEN EXIT ELSE GetAlpha[f]; ENDLOOP; }; seg: Segment segments[s]; end2: EndState GetEndState[seg.p2]; i: Info GetInfo[]; SELECT i.nInts FROM 0 => SELECT TRUE FROM end1.side = out AND end2.side = out => NULL; -- completely out end1.side = in AND end2.side = out, end1.side = out AND end2.side = in => ERROR; -- should have nInt > 0 end1.side = in AND end2.side = in, end1.side = on AND end2.side = in, end1.side = in AND end2.side = on, end1.side = on AND end2.side = on => Add[inside, seg.p1, end1.face]; end1.side = on AND end2.side = out => Add[exit, seg.p1, end1.face]; end1.side = out AND end2.side = on => Add[entry, seg.p2, end2.face]; ENDCASE; 1 => SELECT TRUE FROM end1.side = in AND end2.side = in => ERROR; -- no ints, completely in end1.side = out AND end2.side = out => Add[graze, i.p1, i.f1]; end1.side = out AND end2.side = on, end1.side = out AND end2.side = in => Add[entry, i.p1, i.f1]; end1.side = on AND end2.side = in, end1.side = in AND end2.side = on, end1.side = on AND end2.side = on => Add[inside, seg.p1, end1.face]; end1.side = on AND end2.side = out, end1.side = in AND end2.side = out => { Add[inside, seg.p1, end1.face]; Add[exit, i.p1, i.f1]; }; ENDCASE; 2 => SELECT TRUE FROM end1.side = on AND end2.side = on => Add[inside, seg.p1, end1.face]; end1.side = in AND end2.side = in, end1.side = in AND end2.side = out, end1.side = out AND end2.side = in, end1.side = on AND end2.side = in, end1.side = in AND end2.side = on => ERROR; -- couldn't have 2 ints end1.side = on AND end2.side = out => { Add[inside, seg.p1, end1.face]; Add[exit, i.p2, i.f2]; }; end1.side = out AND end2.side = on => Add[entry, i.p1, i.f1]; end1.side = out AND end2.side = out => { Add[entry, i.p1, i.f1]; Add[exit, i.p2, i.f2]; }; ENDCASE; ENDCASE; end1 end2; ENDLOOP; }; BoundaryIntersectTet: PUBLIC PROC [ tet: REF Tetrahedron, segments: REF Segments, insideToo: BOOL TRUE, scratch: REF TetIntersections NIL] RETURNS [REF TetIntersections] ~ { Next: PROC [i: INT] RETURNS [INT] ~ {RETURN[(i+1) MOD events.length]}; maxD: REAL 0.0; epsilon: REAL 0.01*G3dVector.Distance[tet.a.pos, tet.b.pos]; events: REF Events GetEvents[tet, segments, epsilon, insideToo, ObtainEvents[]]; mark, lastExit, start: INT -1; IF scratch = NIL THEN scratch NEW[TetIntersections]; scratch.length 0; IF events = NIL OR events.length = 0 THEN RETURN[scratch]; FOR i: INT IN [0..events.length) DO type: EventType events[i].type; IF type = graze OR type = exit THEN {mark lastExit i; EXIT}; ENDLOOP; IF mark # -1 THEN FOR i: INT Next[mark], Next[i] DO CheckStart: PROC ~ { DistanceBetweenEntries: PROC [e1, e2: Event] RETURNS [d: REAL] ~ { d G3dVector.Distance[e1.p, segments[e1.seg].p2]+ G3dVector.Distance[e2.p, segments[e2.seg].p1]; FOR s: INT IN (e1.seg..e2.seg) DO d d+segments[s].length; ENDLOOP; }; d: REAL DistanceBetweenEntries[events[lastExit], events[i]]; IF d > maxD THEN {maxD d; start i}; }; SELECT events[i].type FROM graze => {CheckStart[]; lastExit i}; entry => CheckStart[]; exit => lastExit i; ENDCASE; IF i = mark THEN EXIT; ENDLOOP; IF start # -1 THEN FOR i: INT IN [0..events.length) DO e: Event events[start]; scratch AddTetIntersection[scratch, [e.p, e.type = inside, e.face]]; start Next[start]; ENDLOOP; ReleaseEvents[events]; RETURN[scratch]; }; AddTetIntersection: PROC [seq: REF TetIntersections, int: TetIntersection] RETURNS [REF TetIntersections] ~ { IF seq = NIL THEN seq NEW[TetIntersections[3]]; IF seq.length = seq.maxLength THEN { old: REF TetIntersections seq; seq NEW[TetIntersections[MAX[Real.Ceiling[1.3*old.maxLength], 3]]]; FOR i: INT IN [0..old.length) DO seq[i] old[i]; ENDLOOP; seq.length old.length; }; seq[seq.length] int; seq.length seq.length+1; RETURN[seq]; }; TetCenter: PUBLIC PROC [tet: REF Tetrahedron] RETURNS [t: Triple] ~ { t.x 0.25*(tet.a.pos.x+tet.b.pos.x+tet.c.pos.x+tet.d.pos.x); t.y 0.25*(tet.a.pos.y+tet.b.pos.y+tet.c.pos.y+tet.d.pos.y); t.z 0.25*(tet.a.pos.z+tet.b.pos.z+tet.c.pos.z+tet.d.pos.z); }; AddToSegments: PROC [segments: REF Segments, s: Segment] RETURNS [REF Segments] ~ { LengthenSegments: PROC [segments: REF Segments] RETURNS [new: REF Segments] ~ { newLength: NAT MAX[Real.Ceiling[1.3*segments.maxLength], 3]; new NEW[Segments[newLength]]; FOR i: NAT IN [0..segments.length) DO new[i] segments[i]; ENDLOOP; new.length segments.length; }; IF segments = NIL THEN segments NEW[Segments[1]]; IF segments.length = segments.maxLength THEN segments LengthenSegments[segments]; segments[segments.length] s; segments.length segments.length+1; RETURN[segments]; }; scratchTetIntersections: ARRAY [0..10) OF REF TetIntersections ALL[NIL]; ObtainTetIntersections: PUBLIC ENTRY PROC RETURNS [REF TetIntersections] ~ { FOR i: INT IN [0..10) DO s: REF TetIntersections scratchTetIntersections[i]; IF s # NIL THEN {scratchTetIntersections[i] NIL; s.length 0; RETURN[s]}; ENDLOOP; RETURN[NEW[TetIntersections[12]]]; }; ReleaseTetIntersections: PUBLIC ENTRY PROC [scratch: REF TetIntersections] ~ { FOR i: INT IN [0..10) DO IF scratchTetIntersections[i] = NIL THEN {scratchTetIntersections[i] scratch; EXIT}; ENDLOOP; }; END.  ImplicitCubeTetImpl.mesa Copyright c 1992 by Xerox Corporation. All rights reserved. Bloomenthal, February 27, 1993 12:15 pm PST Types and Constants Corners Tetrahedra [Artwork node; type 'Artwork on' to command tool] This should be as fast as possible. Test if plane passes through cube: Test if entire triangle beyond either of tetrahedron's four faces: Test if any point inside tetrahedron: Test if any triangle edge penetrates a tetrahedron face: Test if any tetrahedron edge penetrates the triangle (note, at least a and b already set): Cubes For those desiring an aid to the imagination, here are cut-outs for the tetrahedra that result from the decomposition; the first is the single equilateral tetrahedra in the center of the cube, the second represents the four corner tetrahedra. Try scaling by five. [Artwork node; type 'Artwork on' to command tool] Note: b, c, d to appear cw viewed from a. [Artwork node; type 'Artwork on' to command tool] [Artwork node; type 'Artwork on' to command tool] id [Real.Floor[p.x+0.5], Real.Floor[p.y+0.5], Real.Floor[p.z+0.5]]; id [Real.Round[p.x/size], Real.Round[p.y/size], Real.Round[p.z/size]]; This should be as fast as possible. Test if plane passes through cube: [Artwork node; type 'Artwork on' to command tool] Test if entire triangle beyond either of cube's six faces: Test if any point inside cube: Test if any triangle edge penetrates a cube face: Note: l < r, b < t, n < f Test if any cube edge penetrates the triangle (note, at least lbn and lbf already set): Boundary Procedures Possibilities: no intersections one intersection (grazing), one intersection (entry), one intersection (exit) two intersections (entry and exit) IF i.nInts = 2 AND Eq[i.p1, i.p2] THEN i.nInts 1; (InsideTriangle[] fudge has yielded coincident intersections along tet edge) Search all segments for intersections against all tetrahedral faces. Often this is not needed, but the illustration below, right shows anomolous cases (at patch corners, for example). [Artwork node; type 'Artwork on' to command tool] We assume, however, that the arbitrary nature of the boundary is constrained in one way. If there are no edge intersections, we place no constraints on the boundary (below, left), and any boundary-tetrahedron intersection point serves as entry and exit. If, however, there are edge intersections, we assume that the boundary intersects the tetrahedron in at most a single continuous section (below, right); here, the edge intersection must be incorporated into the boundary section according to the entry and exit points; we assume that these points are separated by the longest outside section (in this case, outside4). [Artwork node; type 'Artwork on' to command tool] Find beginning of chain by finding longest gap from exit to entry: Begin at start and collect points all along chain: BoundaryIntersectTet: PUBLIC PROC [ tet: REF Tetrahedron, segments: REF Segments, mode: TetIntersectMode all, insideToo: BOOL TRUE, f1, f2: TetFace abc, scratch: REF TetIntersections NIL] RETURNS [REF TetIntersections] ~ { Info: TYPE ~ RECORD [p: Triple, f: TetFace, s: INT]; Infos: TYPE ~ RECORD [nInfos: [0..2] 0, infos: ARRAY [0..2) OF Info]; Eq: PROC [s, t: Triple] RETURNS [b: BOOL] ~ {b G3dVector.Distance[s, t] < epsilon}; GetInfos: PROC [start, stop: INT] RETURNS [Infos] ~ { GetInfo: PROC [s: INT] RETURNS [i: Infos] ~ { GetAlpha: PROC [f: TetFace] ~ { t: REF Triangle tet.triangles[f]; d1: REAL G3dPlane.DistanceToPoint[seg.p1, t.plane]; d2: REAL G3dPlane.DistanceToPoint[seg.p2, t.plane]; IF (d1 > 0.0) # (d2 > 0.0) THEN { p: Triple G3dVector.Interp[a2 d1/(d1-d2), seg.p1, seg.p2]; IF NOT Support.InsideTriangle[p, t] THEN RETURN; IF (i.nInfos i.nInfos+1) = 1 THEN { found TRUE; save IF mode = two THEN (IF f = f1 THEN f2 ELSE f1) ELSE f; a1 a2; i.infos[0] [p, f]; } ELSE IF a2 < a1 THEN {i.infos[1] i.infos[0]; i.infos[0] [p, f]} ELSE i.infos[1] [p, f]; IF i.nInfos = 2 AND Eq[i.infos[0].p, i.infos[1].p] THEN { InsideTriangle[] fudge has yielded coincident intersections along tet edge, so don't play trick of limiting faces searched for exit point. i.nInfos 1; found FALSE; }; }; }; a1, a2: REAL; seg: Segment segments[s]; SELECT TRUE FROM found AND mode # all => GetAlpha[save]; found AND mode = all => FOR f: TetFace IN TetFace DO IF f # save AND nInt < 2 THEN GetAlpha[f]; ENDLOOP; mode = two => {GetAlpha[f1]; GetAlpha[f2]}; ENDCASE => FOR f: TetFace IN TetFace DO IF nInt < 2 THEN GetAlpha[f]; ENDLOOP; }; start, stop: INT; save: TetFace abc; found: BOOL FALSE; epsilon: REAL 0.01*G3dVector.Distance[tet.a.pos, tet.b.pos]; IF scratch = NIL THEN scratch ObtainTetIntersections[]; scratch.length 0; FOR s: INT IN [0..segments.length) DO infos: Infos GetInfo[s]; start stop s; SELECT infos.nInfos FROM 1 => { infoStart, infoStop: Info info1; fwd: BOOL Support.InsideTetrahedron[tet, segments[s].p2]; FOR i: INT IF fwd THEN s+1 ELSE segments.length-1, IF fwd THEN i+1 ELSE i-1 DO IF i NOT IN [0..INT[segments.length]) THEN EXIT; IF GetInfo[i] = 0 THEN LOOP; IF fwd THEN {stop i; infoStop info1} ELSE {start i; infoStart info1}; EXIT; ENDLOOP; IF start = stop OR Eq[infoStart.p, infoStop.p] THEN { [] action[info1.p, graze, info1.f]; RETURN; }; IF NOT action[infoStart.p, entry, infoStart.f] THEN RETURN; IF insideToo THEN FOR i: INT IN [start..stop) DO p: Triple segments[i].p2; IF Eq[p,infoStart.p] OR Eq[p,infoStop.p] OR (i>start AND Eq[p,segments[i-1].p2]) THEN LOOP; IF NOT action[segments[i].p2, inside, abc] THEN RETURN; ENDLOOP; [] action[infoStop.p, exit, infoStop.f]; }; 2 => IF action[info1.p, entry, info1.f] THEN [] action[info2.p, exit, info2.f]; ENDCASE => LOOP; EXIT; ENDLOOP; RETURN[scratch]; }; OrderRandomBoundaryIndices: PROC [] ~ { size: INT LengthOfBoundary[]; IF nRandomIndices > size/2 THEN { do it the hard way: allocate a bit buffer, etc. } ELSE { Action: PROC [i: INT] ~ { IF i = 0 THEN hitZero TRUE; IF i = size-1 THEN hitSize TRUE; min1 MIN[min1, i]; max1 MAX[max1, i]; min2 MIN[min2, (i+size/2) MOD size]; max2 MAX[max2, (i+size/2) MOD size]; }; hitZero, hitSize: BOOL FALSE; min1, min2: INT 1000000; max1, max2: INT 0; GetRandomBoundaryIndices[Action]; IF hitZero AND hitSize THEN { max2 (max2+size/2) MOD size; min2 (min2+size/2) MOD size; Process[min2, max2]; } ELSE Process[min1, max1]; }; }; ʴNewlineDelimiter J m1Q.{SY\ZuaT>Q:O>Q\Zuakkxjrj>xO-Sa5g5 T>Q.{SY\ZuaT>Q:O>Q\Zuakkxjrj<O-Sa5g5 T>Q.{SY\ZuaT>Q:O>Q\Zuakkxjrj-Sa5g5 T>Q.{SY\ZuaT>Q:O>Q\Zuakkxjrj-Sa5g5 T>Q.{SY\ZuaT>Q:O>Q\Zuakkxjrj>xO-Sa5g5 T>Q.{SY\ZuaT>Q:O>Q\Zuakkxjrj<O-Sa5g5 T>Q.{SY\ZuaT>Q:O>Q\Zuakkxjrj-Sa5g5 T>Q.{SY\ZuaT>Q:O>Q\Zuakkxjrjy*-Sa5g5 T>Q.{SY\ZuaT>Q:O>Q\Zuakkxjrj>xOy*-Sa5g5 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JcJJ 8J%EJJ 8J.MJJ SJ9YJJJ J J J JJ5JJ+J XJ XJ XJ WJJ%J  J J  J JJ-'J J'LJJJ  JJJJ0.320 0.931 0.362 textColorb## 9 AJ+2J(JJJ@JJ16.0 24 .div 1 1 textColor"J   PJ  J  F%J  #ds1+ J CharProps'*Postfix16.0 24 .div 1 1 textColor*AJyalzQVIkkxjrjV_IzQ 顣VIzQSDgkkxjrjngzQ 顣yalzQomggkkxjrjISVkxZR,kJNSkkxjrjISVk$*g?JNS,k[kkxjrj3A#%ISVkxZR,kJNSkkxjrjZORVk=i4)9"ZR,kkkxjrjVkg?[ZR,kkkxjrj|uMISVkxZR,kJNSkkxjrjMO*Vkg?[ZR,kkkxjrjFy*Vkg?[ZR,kkkxjrj!ISVk$*g?JNS,k[kkxjrjM G [kkxjrj9?"  )9">95kkxjrj(P1 m)P19"kkxjrjZORVkO'#ZR,k{.k#4)P1kkxjrj^py#34,_by[P1Yi#4kkxjrjXiVkYi#4JNS,kkkkkg Interpress90.0 mm xmin 0.0 mm ymin 88.1451 mm xmax 37.06392 mm ymax 39.88614 mm bigger topLeading 39.88614 mm bigger topIndent 1.411111 mm bigger bottomLeading 0.5 0.3 0.95 backgroundColor the topLeading 6 pt .sub backgroundAscent 3 pt backgroundDescent 4 pt outlineBoxThickness 1 pt outlineBoxBearoff7Gargoyle file for scene: stuffed from Gargoyle at November 11, 1992 8:13:06 pm PST Produced by version 9207.29 ViewTransform: [1.0 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