C ALGORITHM 783, COLLECTED ALGORITHMS FROM ACM. C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE, C VOL. 24,NO. 3, September, 1998, P. 261--267. #! /bin/sh # This is a shell archive, meaning: # 1. Remove everything above the #! /bin/sh line. # 2. Save the resulting text in a file. # 3. Execute the file with /bin/sh (not csh) to create the files: # C/ # C/Drivers/ # C/Drivers/Sp/ # C/Drivers/Sp/RES1 # C/Drivers/Sp/RES2 # C/Drivers/Sp/data2 # C/Drivers/Sp/driver1.c # C/Drivers/Sp/driver2.c # C/Src/ # C/Src/Sp/ # C/Src/Sp/src.c # This archive created: Tue Mar 23 08:55:10 1999 export PATH; PATH=/bin:$PATH if test ! -d 'C' then mkdir 'C' fi cd 'C' if test ! -d 'Drivers' then mkdir 'Drivers' fi cd 'Drivers' if test ! -d 'Sp' then mkdir 'Sp' fi cd 'Sp' if test -f 'RES1' then echo shar: will not over-write existing file "'RES1'" else cat << SHAR_EOF > 'RES1' #Inventor V2.0 ascii Separator { Separator { DrawStyle { style LINES } Transform { scaleFactor 2.000000 2.000000 2.000000 } Cube { width 2 height 2 depth 2 } } DEF PATCH Separator { ProfileCoordinate2 { point [ 0.0 3.0 , -3.0 0.0 , 0.0 -3.0 , 3.0 0.0 ] } NurbsProfile { knotVector[ 0, 0, 1, 2, 3, 4, 4] index[ 0, 1, 2, 3, 0] } Coordinate3 { point [ 0.493056 1.868056 0.972222, 0.486111 1.777778 1.111111, 0.333333 1.666667 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1.722499966621399 0.1274999976158142 1.850000023841858 1.127500057220459 0.1850000023841858 1.899999976158142 1.100000023841858 4 3 0.1500000059604645 2 1.850000023841858 0.02250000089406967 1.850000023841858 1.722499966621399 0.1274999976158142 1.850000023841858 1.127500057220459 0.1500000059604645 2 1.149999976158142 0.5 2 1.5 0.8500000238418579 2 1.850000023841858 0.7225000262260437 1.850000023841858 1.977499961853027 0.1274999976158142 1.850000023841858 1.872499942779541 0.1000000014901161 1.899999976158142 1.815000057220459 4 3 0.8500000238418579 2 1.850000023841858 0.7225000262260437 1.850000023841858 1.977499961853027 0.1274999976158142 1.850000023841858 1.872499942779541 0.1500000059604645 2 1.850000023841858 0.5 2 1.5 0.8500000238418579 2 1.149999976158142 0.9775000214576721 1.850000023841858 1.277500033378601 0.8725000023841858 1.850000023841858 1.872499942779541 0.8149999976158142 1.899999976158142 1.899999976158142 4 3 0.8500000238418579 2 1.149999976158142 0.9775000214576721 1.850000023841858 1.277500033378601 0.8725000023841858 1.850000023841858 1.872499942779541 0.8500000238418579 2 1.850000023841858 0.5 2 1.5 0.1500000059604645 2 1.149999976158142 0.2775000035762787 1.850000023841858 1.022500038146973 0.8725000023841858 1.850000023841858 1.127500057220459 0.8999999761581421 1.899999976158142 1.184999942779541 SHAR_EOF fi # end of overwriting check if test -f 'driver1.c' then echo shar: will not over-write existing file "'driver1.c'" else cat << SHAR_EOF > 'driver1.c' /* Driver routine for Pcp2Nurb * generates three Inventor NurbsSurface s * that smooth the corner of a cube with vertices +/-2 * using an adjustable blend ratio with default 0.5. * A fourth biquadratic patch is C1 attached. * * HINT: if confused read the ACM TOMS paper * * Pcp2Nurb: smooth free-form surfacing * with linearly-trimmed bicubic B-splines * by Jorg Peters * * * jorg@cs.purdue.edu Jan 1996 * IRIX 5.3 * COMPILATION and EXECUTION sequence * cc -g -c nurb_iv1.c; cc -g -c pcp2nurb.c; * cc -g -o nurb_iv1 nurb_iv1.o pcp2nurb.o -lm * nurb_iv1 0.5 > out; ivview out; * (try also other values in [0,1]: 0.35 0.65 0.0 1.0 -- * 10 and -10 are not legal values -- so try them, too) */ #define PTS 6 /* number of B-spline control points per row */ #define DEG 3 /* degree of B-spline patch */ #define PFL 4 /* number of points in profile (trimming) curve */ #define KTS DEG+PTS+1 /* number of knots per row */ #define DIM 3 const float m_pi = 3.141592654; void Pcp2Nurb( float Ci[][DIM], int valence[], float ctl_pt[][DIM], float knots[]); main( int argc, char *argv[]) { /*--------------------------VARS------------------------------------*/ /* profile (trimming) curve and control points of NURBS */ float profil[4][2] = { {0,3}, {-3,0}, {0,-3}, {3,0} }; float ctl_pt[PTS*PTS][DIM], knots[KTS]; /* 9 (control and vertex) points of a planar-cut polyhedron * arranged in the order (cf. Figure 5 of the accompanying paper) * 8 7 6 * 1 0 5 4,8 are vertex points * 2 3 4 */ float Pcp[9][DIM] = { { 1, 1, 2}, { -1, 1, 2}, { -1, 2, 1}, { 1, 2, 1}, { 1.333333, 1.333333, 1.333333}, /* V_1 = avg of 1,1,2; 1,2,1; 2,1,1 */ { 2, 1, 1}, { 2,-1, 1}, { 1,-1, 2}, { 0, 0, 2}}; int valence[2] = {3,4}; /* V_1 has 3 neighbors */ /* control points for an abutting biquadratic patch: * reuse Pcp[3], Pcp[0], Pcp[7], Pcp[1], Pcp[2], and * specify 4 additional vertices: */ float Cbi2[4][DIM] = { { -1, -1, 2}, { -3, -1, 2}, { -3, 1, 2}, { -3, 2, 1}}; void draw_rot_patch( float axis[], float angle, float acol[]); void draw_patch( float profil[][2], float ctl_pt[][DIM], float knots[]); void draw_bi2( float ctl_pt[][DIM], float more_ctl_pt[][DIM]); void draw_cube(); float axis[3], acol[3], blend_ratio = 0.5; double atof(); int i; /*------------------------------------------------------------------*/ if (argc > 1) blend_ratio = (float) atof(argv[1]); /* to minimize the amount of code describing the planar cut polyhedron I take advantage of symmetry: */ Pcp[0][0] = Pcp[0][1] = Pcp[3][0] = Pcp[3][2] = Pcp[5][1] = Pcp[5][2] = 2*(1-blend_ratio)+ 0*blend_ratio; /* adjust centroids in case the blend ratio has been changed */ for (i=0; i< 3; i++) { Pcp[4][i] = (Pcp[0][i]+Pcp[3][i]+Pcp[5][i])/3; Pcp[8][i] = (Pcp[1][i]+Pcp[0][i]+Pcp[7][i]+Cbi2[0][i])/4; } /* transform subset Pcp of planar cut polyhedron to a B-spline patch */ Pcp2Nurb(Pcp,valence, ctl_pt, knots); /* write the Inventor file */ printf("#Inventor V2.0 ascii\n\n"); printf("Separator {\n"); draw_cube(); draw_patch(profil,ctl_pt,knots); for (i=0; i<3; i++) axis[i] = 1.0; acol[0]= 0.1; acol[1]= 0.5; acol[2]= 0.7; draw_rot_patch(axis,2*m_pi/3, acol); acol[0]= 0.7; acol[1]= 0.5; acol[2]= 0.1; draw_rot_patch(axis,4*m_pi/3, acol); draw_bi2(Pcp, Cbi2); printf("}\n"); /*------------------------------------------------------------------*/ } void draw_rot_patch( float axis[], float angle, float acol[]) { printf("Separator {\n"); printf("Rotation { rotation %f %f %f %f }\n", axis[0], axis[1], axis[2], angle); printf("Material { ambientColor %f %f %f }\n", acol[0], acol[1], acol[2]); printf("USE PATCH\n"); printf("}\n"); } void draw_patch( float profil[][2], float ctl_pt[][DIM], float knots[]) { int i; printf("DEF PATCH \n"); printf("Separator {\n"); printf("ProfileCoordinate2 {\n"); printf("\tpoint [\n"); for (i=0; i< PFL-1; i++) printf("\t\t%2.1f %2.1f ,\n", profil[i][0], profil[i][1]); i = PFL-1; printf("\t\t%2.1f %2.1f\n", profil[i][0], profil[i][1]); printf("\t]\n"); printf("}\n"); printf("NurbsProfile {\n"); printf("\tknotVector[\n\t 0,"); for (i=0; i<= PFL; i++) printf(" %d,",i); i = PFL; printf(" %d]\n",i); printf("\tindex[\n\t"); for (i=0; i< PFL; i++) printf(" %d,",i); i = 0; printf(" %d]\n",i); printf("}\n"); printf("Coordinate3 {\n"); printf("\tpoint [\n"); for (i=0; i< PTS*PTS-1; i++) printf("\t\t%f %f %f,\n", ctl_pt[i][0], ctl_pt[i][1], ctl_pt[i][2]); i = PTS*PTS-1; printf("\t\t%f %f %f\n", ctl_pt[i][0], ctl_pt[i][1], ctl_pt[i][2]); printf("\t]\n"); printf("}\n"); printf("NurbsSurface {\n"); printf("\tnumUControlPoints\t %d\n", PTS); printf("\tnumVControlPoints\t %d\n", PTS); printf("\tuKnotVector [\n\t\t"); for (i=0; i< KTS-1; i++) printf(" %2.1f,",knots[i]); i = KTS-1; printf(" %2.1f]\n",knots[i]); printf("\n\tvKnotVector [\n\t\t"); for (i=0; i< KTS-1; i++) printf(" %2.1f,",knots[i]); i = KTS-1; printf(" %2.1f]\n",knots[i]); printf("}\n"); printf("}\n"); } void draw_bi2( float ctl_pt[][DIM], float more_ctl_pt[][DIM]) { int i,j,kts,dg; dg = 2; /* surface degree */ printf("Separator {\n"); printf("Material { ambientColor %f %f %f }\n", 1.0, 0.0, 0.0); printf("Coordinate3 {\n"); printf("\tpoint [\n"); i = 7; printf("\t\t%f %f %f,\n", ctl_pt[i][0], ctl_pt[i][1], ctl_pt[i][2]); i = 0; printf("\t\t%f %f %f,\n", ctl_pt[i][0], ctl_pt[i][1], ctl_pt[i][2]); i = 3; printf("\t\t%f %f %f,\n", ctl_pt[i][0], ctl_pt[i][1], ctl_pt[i][2]); j = 0; printf("\t\t%f %f %f,\n", more_ctl_pt[j][0], more_ctl_pt[j][1], more_ctl_pt[j][2]); i = 1; printf("\t\t%f %f %f,\n", ctl_pt[i][0], ctl_pt[i][1], ctl_pt[i][2]); i = 2; printf("\t\t%f %f %f,\n", ctl_pt[i][0], ctl_pt[i][1], ctl_pt[i][2]); j = 1; printf("\t\t%f %f %f,\n", more_ctl_pt[j][0], more_ctl_pt[j][1], more_ctl_pt[j][2]); j = 2; printf("\t\t%f %f %f,\n", more_ctl_pt[j][0], more_ctl_pt[j][1], more_ctl_pt[j][2]); j = 3; printf("\t\t%f %f %f\n", more_ctl_pt[j][0], more_ctl_pt[j][1], more_ctl_pt[j][2]); printf("\t]\n"); printf("}\n"); kts = dg+3+1; /* number of knots in row = dg + coeffs + 1 */ printf("NurbsSurface {\n"); printf("\tnumUControlPoints\t %d\n", dg+1); printf("\tnumVControlPoints\t %d\n", dg+1); printf("\tuKnotVector [\n\t\t"); for (i=0; i< kts-1; i++) printf(" %2.1f,",1.0*i); i = kts-1; printf(" %2.1f]\n",1.0*i); printf("\n\tvKnotVector [\n\t\t"); for (i=0; i< kts-1; i++) printf(" %2.1f,",1.0*i); i = kts-1; printf(" %2.1f]\n",1.0*i); printf("}\n"); printf("}\n"); } /* write Inventor node for cube */ void draw_cube() { printf("Separator {\n"); printf("DrawStyle {\n"); printf("\tstyle LINES \n"); printf("}\n"); printf("Transform {\n"); printf("\tscaleFactor %f %f %f\n",2.0,2.0,2.0); printf("}\n"); printf("Cube {\n"); printf("\t width 2 \n"); printf("\t height 2 \n"); printf("\t depth 2 \n"); printf("}\n"); printf("}\n"); } SHAR_EOF fi # end of overwriting check if test -f 'driver2.c' then echo shar: will not over-write existing file "'driver2.c'" else cat << SHAR_EOF > 'driver2.c' /* Driver routine for Pcp2Nurb * * generates a twisted cube from a planar cut polyhedron (pcp) * to illustrate surface of medium complexity * * HINT: if confused read the ACM TOMS paper * * Pcp2Nurb: smooth free-form surfacing * with linearly-trimmed bicubic B-splines * by Jorg Peters * * input: file with (72) pcp subnets * output: Open Inventor NurbsSurfaces * * jorg@cs.purdue.edu Jan 1996 * IRIX 5.3 * COMPILATION and EXECUTION sequence * cc -g -c nurb_iv2.c; cc -g -c pcp2nurb.c; * cc -g -o nurb_iv2 nurb_iv2.o pcp2nurb.o -lm * nurb_iv2 < in2 > out; ivview out; */ #define PTS 6 /* number of B-spline control points per row */ #define DEG 3 /* degree of B-spline patch */ #define PFL 4 /* number of points in profile (trimming) curve */ #define KTS DEG+PTS+1 /* number of knots per row */ #define DIM 3 #define SUB 9 /* size of subnet */ void Pcp2Nurb( float Ci[][DIM], int valence[], float ctl_pt[][DIM], float knots[]); main() { /*--------------------------VARS------------------------------------*/ /* nine-point subnet */ float Pcp[SUB][DIM]; int valence[2]; /* profile (trimming) curve and control points of NURBS */ float profil[4][2] = { {0,3}, {-3,0}, {0,-3}, {3,0} }; float ctl_pt[PTS*PTS][DIM], knots[KTS]; int i,j, no_subnets; void draw_patch( float profil[][2], float ctl_pt[][DIM], float knots[]); /*------------------------------------------------------------------*/ /* write the Inventor file */ printf("#Inventor V2.0 ascii\n\n"); printf("Separator {\n"); scanf("%d", &no_subnets); for (i=0; i< no_subnets; i++) { scanf("%d %d",&valence[0], &valence[1]); for (j=0; j< SUB; j++) scanf("%f %f %f",&Pcp[j][0], &Pcp[j][1], &Pcp[j][2]); /* transform subset Pcp of planar cut polyhedron to a B-spline patch */ Pcp2Nurb(Pcp,valence, ctl_pt, knots); draw_patch(profil,ctl_pt,knots); } printf("}\n"); /*------------------------------------------------------------------*/ } void draw_patch( float profil[][2], float ctl_pt[][DIM], float knots[]) { int i; printf("Separator {\n"); printf("Material { ambientColor %f %f %f }\n", 0.8, 0.1, 0.0); printf("ProfileCoordinate2 {\n"); printf("\tpoint [\n"); for (i=0; i< PFL-1; i++) printf("\t\t%2.1f %2.1f ,\n", profil[i][0], profil[i][1]); i = PFL-1; printf("\t\t%2.1f %2.1f\n", profil[i][0], profil[i][1]); printf("\t]\n"); printf("}\n"); printf("NurbsProfile {\n"); printf("\tknotVector[\n\t 0,"); for (i=0; i<= PFL; i++) printf(" %d,",i); i = PFL; printf(" %d]\n",i); printf("\tindex[\n\t"); for (i=0; i< PFL; i++) printf(" %d,",i); i = 0; printf(" %d]\n",i); printf("}\n"); printf("Coordinate3 {\n"); printf("\tpoint [\n"); for (i=0; i< PTS*PTS-1; i++) printf("\t\t%f %f %f,\n", ctl_pt[i][0], ctl_pt[i][1], ctl_pt[i][2]); i = PTS*PTS-1; printf("\t\t%f %f %f\n", ctl_pt[i][0], ctl_pt[i][1], ctl_pt[i][2]); printf("\t]\n"); printf("}\n"); printf("NurbsSurface {\n"); printf("\tnumUControlPoints\t %d\n", PTS); printf("\tnumVControlPoints\t %d\n", PTS); printf("\tuKnotVector [\n\t\t"); for (i=0; i< KTS-1; i++) printf(" %2.1f,",knots[i]); i = KTS-1; printf(" %2.1f]\n",knots[i]); printf("\n\tvKnotVector [\n\t\t"); for (i=0; i< KTS-1; i++) printf(" %2.1f,",knots[i]); i = KTS-1; printf(" %2.1f]\n",knots[i]); printf("}\n"); printf("}\n"); } SHAR_EOF fi # end of overwriting check cd .. cd .. if test ! -d 'Src' then mkdir 'Src' fi cd 'Src' if test ! -d 'Sp' then mkdir 'Sp' fi cd 'Sp' if test -f 'src.c' then echo shar: will not over-write existing file "'src.c'" else cat << SHAR_EOF > 'src.c' /* Pcp2Nurb: * convert submesh of a planar cut polyhedron (pcp) into a nurbs patch * * A pcp is a polyhedron with every interior vertex surrounded * by four facets. The first and third facet are * four-sided, the other two must be planar affine $n$-gons if they * have more than four edges. * * generated by jorg@cs.purdue.edu * all commercial rights reserved! * * Input : Ci -- 9-point subnet of a pcp * valence -- number of patches joining at the vertex * Output: ctl_pt -- 36 B-spline control points * knots -- knot sequence * * cf the sample driver routines in nurb_iv{1,2}.c * * Example pcp obtained by chopping a cube corner; * the subnet is C0,C1,...,C8 * * * +---------------------------C7 * / / \ * / C8 / \ * / / C6 * C1--------------------------C0 / | * / /\ / | * / /C4 \ / | * C2--------------------------C3----C5 | * | | | | * | | | | * | | | / * | | | / * | | | / * | | |/ * +---------------------------+ - - * * HINT: more information can be found in the ACM TOMS paper * * Pcp2Nurb: smooth free-form surfacing * with linearly-trimmed bicubic B-splines * by Jorg Peters * and a preprint on the authors homepage * (the example appears as Figure 5) * HINT: there are >= 2 driver routines this subroutine * HINT: while the orientation of the input subnet does * not matter to the routine inside/outside coloring * of your display may be affected */ #include #define DIM 3 void Pcp2Nurb(float Ci[][DIM], int valence[], float ctl_pt[][DIM], float knots[]) { float t0,c[4]; int m; double mypi = 4*atan(1.0); float myknots[10] = { -3,-3,-3,-3,0,0,3,3,3,3 }; c[1] = cos(2*mypi/valence[0]); c[3] = cos(2*mypi/valence[1]); for (m=0; m<10;m++) knots[m] = myknots[m]; for (m=0; m