DIRECTORY RealFns USING [CosDeg, SinDeg, SqRt], ThreeDPackage; ThreeDPackageImpl: CEDAR PROGRAM IMPORTS RealFns EXPORTS ThreeDPackage = BEGIN OPEN ThreeDPackage; Sqr: PROCEDURE [number: REAL] RETURNS [REAL] ~ INLINE { RETURN[number * number]; }; SumTriple: PUBLIC PROCEDURE [t1, t2: Triple] RETURNS [Triple] ~ { RETURN[ [t1.x + t2.x, t1.y + t2.y, t1.z + t2.z] ]; }; DiffTriple: PUBLIC PROCEDURE [t1, t2: Triple] RETURNS [Triple] ~ { RETURN[ [t1.x - t2.x, t1.y - t2.y, t1.z - t2.z] ]; }; ScaleTriple: PUBLIC PROCEDURE [t: Triple, s: REAL] RETURNS [Triple] ~ { RETURN[ [t.x * s, t.y * s, t.z * s] ]; }; Normalize: PUBLIC PROC[v: Triple] RETURNS[Triple] ~ { mag: REAL _ RealFns.SqRt[v.x * v.x + v.y * v.y + v.z * v.z]; IF mag <= 0. THEN mag _ 1.; RETURN [ [v.x/mag, v.y/mag, v.z/mag] ]; }; DotProd: PUBLIC PROC[v1, v2: Triple] RETURNS [REAL] ~ { RETURN [v1.x * v2.x + v1.y * v2.y + v1.z * v2.z]; }; CrossProd: PUBLIC PROC[v1, v2: Triple] RETURNS [vOut: Triple] ~ { vOut.x _ v1.y*v2.z - v1.z*v2.y; vOut.y _ v1.z*v2.x - v1.x*v2.z; vOut.z _ v1.x*v2.y - v1.y*v2.x; }; GetIDTransform: PUBLIC PROC[] RETURNS[id: Transformation3D] ~ { id.a _ [1., 0., 0., 0.]; id.b _ [0., 1., 0., 0.]; id.c _ [0., 0., 1., 0.]; id.d _ [0., 0., 0., 1.]; }; ConcatT: PUBLIC PROC[xfm1, xfm2: Transformation3D] RETURNS[xfmOut: Transformation3D] ~{ QuadProd: PROC[q1, q2: Quad] RETURNS [REAL] = INLINE { RETURN [q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w]; }; col2x, col2y, col2z, col2w: Quad; col2x _ [xfm2.a.x, xfm2.b.x, xfm2.c.x, xfm2.d.x]; col2y _ [xfm2.a.y, xfm2.b.y, xfm2.c.y, xfm2.d.y]; col2z _ [xfm2.a.z, xfm2.b.z, xfm2.c.z, xfm2.d.z]; col2w _ [xfm2.a.w, xfm2.b.w, xfm2.c.w, xfm2.d.w]; xfmOut.a.x _ QuadProd[xfm1.a, col2x]; xfmOut.a.y _ QuadProd[xfm1.a, col2y]; xfmOut.a.z _ QuadProd[xfm1.a, col2z]; xfmOut.a.w _ QuadProd[xfm1.a, col2w]; xfmOut.b.x _ QuadProd[xfm1.b, col2x]; xfmOut.b.y _ QuadProd[xfm1.b, col2y]; xfmOut.b.z _ QuadProd[xfm1.b, col2z]; xfmOut.b.w _ QuadProd[xfm1.b, col2w]; xfmOut.c.x _ QuadProd[xfm1.c, col2x]; xfmOut.c.y _ QuadProd[xfm1.c, col2y]; xfmOut.c.z _ QuadProd[xfm1.c, col2z]; xfmOut.c.w _ QuadProd[xfm1.c, col2w]; xfmOut.d.x _ QuadProd[xfm1.d, col2x]; xfmOut.d.y _ QuadProd[xfm1.d, col2y]; xfmOut.d.z _ QuadProd[xfm1.d, col2z]; xfmOut.d.w _ QuadProd[xfm1.d, col2w]; }; Transform3D: PUBLIC PROC[ vtx: Triple, xfm: Transformation3D] RETURNS [t: Triple] ~ { t.x _ xfm.a.x * vtx.x + xfm.b.x * vtx.y + xfm.c.x * vtx.z + xfm.d.x; t.y _ xfm.a.y * vtx.x + xfm.b.y * vtx.y + xfm.c.y * vtx.z + xfm.d.y; t.z _ xfm.a.z * vtx.x + xfm.b.z * vtx.y + xfm.c.z * vtx.z + xfm.d.z; }; TransformVec3D: PUBLIC PROC[ vtx: Triple, xfm: Transformation3D] RETURNS [t: Triple] ~ { t.x _ xfm.a.x * vtx.x + xfm.b.x * vtx.y + xfm.c.x * vtx.z; t.y _ xfm.a.y * vtx.x + xfm.b.y * vtx.y + xfm.c.y * vtx.z; t.z _ xfm.a.z * vtx.x + xfm.b.z * vtx.y + xfm.c.z * vtx.z; }; Translate3D: PUBLIC PROC[ delta: Triple] RETURNS [xfm: Transformation3D] ~ { xfm _ GetIDTransform[]; xfm.d _ [delta.x, delta.y, delta.z, 1.]; }; Rotate3D: PUBLIC PROC[base, axis: Triple, theta: REAL] RETURNS[Transformation3D] ~ { xfm, mtx: Transformation3D _ GetIDTransform[]; cosTheta: REAL _ RealFns.CosDeg[theta]; sinTheta: REAL _ RealFns.SinDeg[theta]; xfm.d.x _ -base.x; xfm.d.y _ -base.y; xfm.d.z _ -base.z; axis _ Normalize[axis]; mtx.a.x _ Sqr[axis.x] + (1.0 - Sqr[axis.x]) * cosTheta; mtx.b.y _ Sqr[axis.y] + (1.0 - Sqr[axis.y]) * cosTheta; mtx.c.z _ Sqr[axis.z] + (1.0 - Sqr[axis.z]) * cosTheta; mtx.b.x _ axis.x * axis.y * (1.0 - cosTheta) + axis.z * sinTheta; mtx.a.y _ axis.x * axis.y * (1.0 - cosTheta) - axis.z * sinTheta; mtx.c.x _ axis.x * axis.z * (1.0 - cosTheta) - axis.y * sinTheta; mtx.a.z _ axis.x * axis.z * (1.0 - cosTheta) + axis.y * sinTheta; mtx.c.y _ axis.y * axis.z * (1.0 - cosTheta) + axis.x * sinTheta; mtx.b.z _ axis.y * axis.z * (1.0 - cosTheta) - axis.x * sinTheta; xfm _ ConcatT[xfm, mtx]; mtx _ GetIDTransform[]; mtx.d.x _ base.x; mtx.d.y _ base.y; mtx.d.z _ base.z; xfm _ ConcatT[xfm, mtx]; RETURN[xfm]; }; END. LThreeDPackageImpl.mesa Last Edited by: Crow, December 5, 1983 7:51 pm Ê5˜headšœ™Jšœ.™.J˜šÏk ˜ Jšœœ˜(Jšœ˜—J˜—head2šœœ˜ Iašœ˜Mšœ˜J˜Jšœœ ˜J˜—IunitšÏnœ œ œœœœœ˜Sšž œœœ ˜AJšœ1˜7—šž œœœ ˜BJšœ0˜6—š žœœ œœœ ˜GJšœ$˜*—šž œœœ˜7Mšœœ5˜>Mšœœ ˜Mšœ!˜'Mšœ˜—šžœœœœ˜9Mšœ,˜2Mšœ˜—šž œœœ˜AM˜J˜J˜Jšœ˜—šžœœœ˜?M˜M˜M˜M˜M˜—šžœœœ˜Wš žœœœœœ˜6Mšœ?˜E—M˜!N˜1M˜1M˜1M˜1NšœL˜LMšœN˜NNšœK˜KMšœN˜NNšœL˜LMšœN˜NNšœK˜KMšœN˜NM˜—šžœœ&œ˜UJšœD˜DJšœD˜DJšœD˜DJ˜—šžœœ&œ˜XJšœ:˜:Jšœ:˜:Jšœ:˜:Jšœ˜—šžœœœœ˜LMšœ˜Mšœ(˜(Mšœ˜—š žœœœœœ˜TJ˜.Jšœ œ˜'Jšœ œ˜'J˜J˜>J˜J˜7J˜7J˜7J˜J˜BJ˜BJ˜J˜AJ˜AJ˜J˜BJ˜AJ˜J˜J˜J˜;J˜Jšœ˜J˜J˜—Jšœ˜—…—Ü]