#include #include "irit_sm.h" #include "extra_fn.h" /* * bzrintrp.c: * Bezier curve interpolation routines. From Graphics Gems 3. */ /***************************************************************************** The following arrays were created by symbolically solving the bezier interpolant problem for orders 2 to 9. Each line holds the weights for the given points to interpolate at node values (i/k, k is the degree) as the i'th element divided by the zero element in line. *****************************************************************************/ static long IB2[2][3] = { { 1L, 1L, 0L }, { 1L, 0L, 1L } }; static long *InterpBlend2[2] = { IB2[0], IB2[1] }; static long IB3[3][4] = { { 1L, 1L, 0L, 0L }, { 2L, -1L, 4L, -1L }, { 1L, 0L, 0L, 1L } }; static long *InterpBlend3[3] = { IB3[0], IB3[1], IB3[2] }; static long IB4[4][5] = { { 1L, 1L, 0L, 0L, 0L }, { 6L, -5L, 18L, -9L, 2L }, { 6L, 2L, -9L, 18L, -5L }, { 1L, 0L, 0L, 0L, 1L } }; static long *InterpBlend4[4] = { IB4[0], IB4[1], IB4[2], IB4[3] }; static long IB5[5][6] = { { 1L, 1L, 0L, 0L, 0L, 0L }, { 12L, -13L, 48L, -36L, 16L, -3L }, { 18L, 13L, -64L, 120L, -64L, 13L }, { 12L, -3L, 16L, -36L, 48L, -13L }, { 1L, 0L, 0L, 0L, 0L, 1L } }; static long *InterpBlend5[5] = { IB5[0], IB5[1], IB5[2], IB5[3], IB5[4] }; static long IB6[6][7] = { { 1L, 1L, 0L, 0L, 0L, 0L, 0L }, { 60L, -77L, 300L, -300L, 200L, -75L, 12L }, { 240L, 269L, -1450L, 2950L, -2300L, 925L, -154L }, { 240L, -154L, 925L, -2300L, 2950L, -1450L, 269L }, { 60L, 12L, -75L, 200L, -300L, 300L, -77L }, { 1L, 0L, 0L, 0L, 0L, 0L, 1L } }; static long *InterpBlend6[6] = { IB6[0], IB6[1], IB6[2], IB6[3], IB6[4], IB6[5] }; static long IB7[7][8] = { { 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L }, { 60L, -87L, 360L, -450L, 400L, -225L, 72L, -10L }, { 150L, 227L, -1332L, 3015L, -3080L, 1845L, -612L, 87L }, { 200L, -227L, 1512L, -4185L, 6000L, -4185L, 1512L, -227L }, { 150L, 87L, -612L, 1845L, -3080L, 3015L, -1332L, 227L }, { 60L, -10L, 72L, -225L, 400L, -450L, 360L, -87L }, { 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L } }; static long *InterpBlend7[7] = { IB7[0], IB7[1], IB7[2], IB7[3], IB7[4], IB7[5], IB7[6] }; static long IB8[8][9] = { { 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L }, { 420L, -669L, 2940L, -4410L, 4900L, -3675L, 1764L, -490L, 60L }, { 7560L, 14318L, -90846L, 228879L, -288610L, 229320L, -113778L, 32291L, -4014L }, { 25200L, -42881L, 313012L, -960351L, 1568980L,-1409975L, 750876L, -223097L, 26836L }, { 25200L, 28636L, -223097L, 750876L,-1409975L, 1568980L, -960351L, 313012L, -42881L }, { 7560L, -4014L, 32291L, -113778L, 229320L, -288610L, 228879L, -90846L, 14318L }, { 420L, 60L, -490L, 1764L, -3675L, 4900L, -4410L, 2940L, -669L }, { 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L } }; static long *InterpBlend8[8] = { IB8[0], IB8[1], IB8[2], IB8[3], IB8[4], IB8[5], IB8[6], IB8[7] }; static long IB9[9][10] = { { 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L }, { 840L, -1443L, 6720L, -11760L, 15680L, -14700L, 9408L, -3920L, 960L, -105L }, { 8820L, 19939L, -135936L, 379008L, -568064L, 561960L, -370944L, 157696L, -39168L, 4329L }, { 17640L, -40953L, 324544L,-1096144L, 2030784L,-2229500L, 1563968L, -691824L, 176704L, -19939L }, { 22050L, 40953L, -349184L, 1298304L,-2731008L, 3503920L,-2731008L, 1298304L, -349184L, 40953L }, { 17640L, -19939L, 176704L, -691824L, 1563968L,-2229500L, 2030784L, -1096144L, 324544L, -40953L }, { 8820L, 4329L, -39168L, 157696L, -370944L, 561960L, -568064L, 379008L, -135936L, 19939L }, { 840L, -105L, 960L, -3920L, 9408L, -14700L, 15680L, -11760L, 6720L, -1443L }, { 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L } }; static long *InterpBlend9[9] = { IB9[0], IB9[1], IB9[2], IB9[3], IB9[4], IB9[5], IB9[6], IB9[7], IB9[8] }; static long **InterpBlend[] = { NULL, NULL, InterpBlend2, InterpBlend3, InterpBlend4, InterpBlend5, InterpBlend6, InterpBlend7, InterpBlend8, InterpBlend9 }; /***************************************************************************** * DESCRIPTION: * * Blends one point using Input and Interp arrays. * * * * PARAMETERS: * * Input: Points to interpolate at node parameter values. * * Interp: One raw from the above matrix of size Size. * * Size: Size of control polygon which is same as matrix size. * * * * RETURN VALUE: * * RealType: The interpolated control point. * *****************************************************************************/ static RealType BzrCrvInterpOnePoint(RealType *Input, long *Interp, int Size) { int i; long Denom = *Interp++; RealType R = 0.0; for (i = 0; i < Size; i++) R += (*Input++ * (RealType) (*Interp++)) / ((RealType) Denom); return R; } /***************************************************************************** * DESCRIPTION: M * Blends the input points using the Interp array and puts the resulted M * blended point in Result array. Input and Result array are of size Size. M * * * PARAMETERS: M * Result: Where the interpolated control points will be placed. M * Input: Points to interpolate at node parameter values. M * Size: Of control polygon. M * * * RETURN VALUE: M * void M * * * KEYWORDS: M * BzrCrvInterp, interpolation M *****************************************************************************/ void BzrCrvInterp(RealType *Result, RealType *Input, int Size) { int i; long **Interp = InterpBlend[Size]; if (Size < 2 || Size > 9) return; for (i = 0; i < Size; i++) *Result++ = BzrCrvInterpOnePoint(Input, *Interp++, Size); }