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authorJonathan deWerd <jjoonathan@gmail.com>2014-07-23 07:27:48 +0400
committerJonathan deWerd <jjoonathan@gmail.com>2014-07-23 07:27:48 +0400
commita0ed39729a7e47240fd18915d6eaed378455181e (patch)
tree25205ef6c9fdb2695c8cb0b4a8a658863acb6289
parent6103835784c456d1fc7d0bfb2ae6d6dde8335763 (diff)
NURBS surf eval + derivatives written (not verified), basis cache.
Diffstat
-rw-r--r--source/blender/blenkernel/intern/curve_eval.cpp112
-rw-r--r--tests/interactive/curve_eval.h14
-rw-r--r--tests/interactive/nurbs_derivative_eval.cpp78
-rw-r--r--tests/interactive/nurbs_eval.nb2685
4 files changed, 1859 insertions, 1030 deletions
diff --git a/source/blender/blenkernel/intern/curve_eval.cpp b/source/blender/blenkernel/intern/curve_eval.cpp
index 7c883c90db9..cbd2396ee63 100644
--- a/source/blender/blenkernel/intern/curve_eval.cpp
+++ b/source/blender/blenkernel/intern/curve_eval.cpp
@@ -30,6 +30,7 @@
*/
#include <stdlib.h>
#include <stdio.h>
+#include <math.h>
#if defined(NURBS_eval_test)
#include "curve_eval.h"
@@ -241,6 +242,7 @@ void BKE_bspline_basis_eval(float u, int i, float *U, int num_pts, int order, in
/* Compute N(i-j+r, j, u) */
ndu[j][r] = right[r+1]+left[j-r];
temp = ndu[r][j-1]/ndu[j][r];
+ if (!isfinite(temp)) temp=0;
ndu[r][j] = saved+right[r+1]*temp; /* N(i-p+r,j,u) */
saved = left[j-r]*temp;
}
@@ -260,16 +262,19 @@ void BKE_bspline_basis_eval(float u, int i, float *U, int num_pts, int order, in
int rk=r-k, pk=p-k, j=0;
if (r>=k) {
a[s2][0] = a[s1][0]/ndu[pk+1][rk];
+ if (!isfinite(a[s2][0])) a[s2][0]=0;
d = a[s2][0]*ndu[rk][pk];
}
j1 = (rk>=-1)? 1 : -rk;
j2 = (r-1<=pk)? k-1 : p-r;
for (j=j1; j<=j2; j++) {
a[s2][j] = (a[s1][j]-a[s1][j-1])/ndu[pk+1][rk+j];
+ if (!isfinite(a[s2][j])) a[s2][j]=0;
d += a[s2][j]*ndu[rk+j][pk];
}
if (r<=pk) {
a[s2][k] = -a[s1][k-1]/ndu[pk+1][r];
+ if (!isfinite(a[s2][k])) a[s2][k]=0;
d += a[s2][k]*ndu[r][pk];
}
out[k][r] = d;
@@ -297,8 +302,9 @@ void BKE_bspline_basis_eval(float u, int i, float *U, int num_pts, int order, in
* P,stride: P[0], P[stride], ..., P[(num_pts-1)*stride] are the ctrl points
* nd: number of derivatives to calculate
* out: out[0], out[1], ..., out[nd] are the evaluated points/derivatives
+ * premultiply_weights: multiply x,y,z coords by w. If in doubt, pass "false".
*/
-void BKE_bspline_curve_eval(float u, float *U, int num_pts, int order, BPoint *P, int stride, int nd, BPoint *out)
+void BKE_bspline_curve_eval(float u, float *U, int num_pts, int order, BPoint *P, int stride, int nd, BPoint *out, bool premultiply_weights)
{
int p = order-1;
if (!(nd<=p)) {
@@ -311,9 +317,16 @@ void BKE_bspline_curve_eval(float u, float *U, int num_pts, int order, BPoint *P
BKE_bspline_basis_eval(u, i, U, num_pts, order, nd, basisu);
for (int d=0; d<=nd; d++) { /* calculate derivative d */
float accum[4] = {0,0,0,0};
- for (int j=0; j<=p; j++)
- madd_v4_v4fl(accum, P[(i-p+j)*stride].vec, basisu[d][j]);
- madd_v4_v4fl(out[d].vec, accum, 1.0);
+ for (int j=0; j<=p; j++) {
+ float N = basisu[d][j];
+ float *pt = P[(i-p+j)*stride].vec;
+ float w = (premultiply_weights)? pt[3] : 1.0;
+ accum[0] += pt[0]*w*N;
+ accum[1] += pt[1]*w*N;
+ accum[2] += pt[2]*w*N;
+ accum[3] += pt[3]*N;
+ }
+ mul_v4_v4fl(out[d].vec, accum, 1.0);
}
}
@@ -325,9 +338,10 @@ void BKE_bspline_curve_eval(float u, float *U, int num_pts, int order, BPoint *P
void BKE_nurbs_curve_eval(float u, float *U, int num_pts, int order, BPoint *P, int stride, int nd, BPoint *out)
{
/* Get Cw, Cw^(1), ..., Cw^(nd). Cw^(i) gives both A^(i)(u) and w^(i)(u). */
- BKE_bspline_curve_eval(u, U, num_pts, order, P, stride, nd, out);
+ BKE_bspline_curve_eval(u, U, num_pts, order, P, stride, nd, out, true);
for (int k=0; k<=nd; k++) {
- float v[4]; mul_v4_v4fl(v, out[k].vec, 1.0);
+ float *Ak = out[k].vec;
+ float v[4] = {Ak[0], Ak[1], Ak[2], Ak[3]};
for (int i=1; i<=k; i++) {
int kCi = BKE_nurb_binom_coeff(k, i);
float wi = out[i].vec[3];
@@ -347,19 +361,35 @@ void BKE_nurbs_curve_eval(float u, float *U, int num_pts, int order, BPoint *P,
* nd: (#calc'd derivatives in u direction + # calc'd derivatives in v direction <= nd)
* out: S(u,v), Su(u,v),Sv(u,v), Suu(u,v),Suv(u,v),Svv(u,v), ...
* out[nuv*(nuv+1)/2 + nv] is the pt with nuv u+v partials, nv v partials
+ * premultiply_weights: multiply x,y,z coords by w. If in doubt, pass "false".
+ * cache: share a BSplineCacheU object to make evaling multiple pts at same u coord efficient
*/
void BKE_bspline_surf_eval(float u, float v,
int pntsu, int orderu, float *U,
int pntsv, int orderv, float *V,
- BPoint *P, int nd, BPoint *out) {
+ BPoint *P, int nd, BPoint *out, bool premultiply_weights,
+ BSplineCacheU *ucache) {
int pu=orderu-1, pv=orderv-1;
if (!(nd<=orderu-1 && nd<=orderv-1)) {
fprintf(stderr, "NURBS eval error: surf requested too many derivatives\n");
return;
}
- float Nu[NURBS_MAX_ORDER][NURBS_MAX_ORDER];
- int iu = BKE_bspline_nz_basis_range(u, U, pntsu, orderu);
- BKE_bspline_basis_eval(u, iu, U, pntsu, orderu, nd, Nu);
+ float Nu_local[NURBS_MAX_ORDER][NURBS_MAX_ORDER];
+ float (*Nu)[NURBS_MAX_ORDER] = Nu_local;
+ int iu = -1;
+ if (ucache) {
+ Nu = ucache->Nu;
+ if (ucache->u==u) { // Cache Hit
+ iu = ucache->iu;
+ } else { // Cache miss
+ ucache->u = u;
+ iu = ucache->iu = BKE_bspline_nz_basis_range(u, U, pntsu, orderu);
+ BKE_bspline_basis_eval(u, iu, U, pntsu, orderu, nd, Nu);
+ }
+ } else { // No cache
+ iu = BKE_bspline_nz_basis_range(u, U, pntsu, orderu);
+ BKE_bspline_basis_eval(u, iu, U, pntsu, orderu, nd, Nu);
+ }
float Nv[NURBS_MAX_ORDER][NURBS_MAX_ORDER];
int iv = BKE_bspline_nz_basis_range(v, V, pntsv, orderv);
BKE_bspline_basis_eval(v, iv, V, pntsv, orderv, nd, Nv);
@@ -367,23 +397,73 @@ void BKE_bspline_surf_eval(float u, float v,
float iut=0; for (int i=0; i<orderu; i++) iut+=Nu[0][i];
int outidx=0;
- for (int nuv=0; nuv<=nd; nuv++) {
- for (int nv=0; nv<=nuv; nv++) {
+ for (int nuv=0; nuv<=nd; nuv++) { // nuv = (# u derivs)+(#v derivs)
+ for (int nv=0; nv<=nuv; nv++) { // nv = #v derivs
int nu = nuv-nv;
- /* nu = # derivs in u direction nv = # derivs in v direction */
float accum[4] = {0,0,0,0};
- double basis_sum=0;
for (int i=iu-pu; i<=iu; i++) {
for (int j=iv-pv; j<=iv; j++) {
+ // i,j index into the global (0 to pnts{u,v}-1) basis list
+ // ii,jj index into the nonzero stretch (N_i-p) to N_i for u in [u_i, u_i+1).)
int ii=i-(iu-pu), jj=j-(iv-pv);
float basis = Nu[nu][ii]*Nv[nv][jj];
float *ctrlpt = P[pntsu*j+i].vec;
- madd_v4_v4fl(accum, ctrlpt, basis);
- basis_sum += basis;
+ float w = (premultiply_weights)? ctrlpt[3] : 1.0;
+ accum[0] += ctrlpt[0]*basis*w;
+ accum[1] += ctrlpt[1]*basis*w;
+ accum[2] += ctrlpt[2]*basis*w;
+ accum[3] += ctrlpt[3]*basis;
}
}
mul_v4_v4fl(out[outidx].vec, accum, 1.0);
outidx++;
}
}
+}
+
+#define Skl(k,l) out[((k)+(l))*((k)+(l)+1)/2+(l)].vec
+/* Evaluates a NURBS surface and nd of its partial derivatives at (u,v).
+ * (u,v): the point in parameter space being pushed through the map
+ * pntsu,orderu,U: # control points, order, knots in the U direction
+ * pntsv,orderv,V: # control points, order, knots in the V direction
+ * P: points of the control polygon packed in u-major order:
+ * P[0]~u0v0 P[1]~u1v0 ... P[pntsu-1]~u(pntsu-1)v0
+ * P[pntsu]~u0v1 P[pntsu+1]~u1v1 ... P[2*pntsu-1]~u(pntsu-1)v1 ...
+ * nd: (#calc'd derivatives in u direction + # calc'd derivatives in v direction <= nd)
+ * out: S(u,v), Su(u,v),Sv(u,v), Suu(u,v),Suv(u,v),Svv(u,v), ...
+ * out[nuv*(nuv+1)/2 + nv] is the pt with nuv u+v partials, nv v partials
+ */
+void BKE_nurbs_surf_eval(float u, float v,
+ int pntsu, int orderu, float *U,
+ int pntsv, int orderv, float *V,
+ BPoint *P, int nd, BPoint *out, BSplineCacheU *ucache) {
+ // Let S(nu,nv) denote (d/du)^nu (d/dv)^nv S(u,v)->(x,y,z)
+ // Let A(nu,nv) denote (d/du)^nu (d/dv)^nv A(u,v)->(wx,wy,wz)
+ // First, calculate A
+ BKE_bspline_surf_eval(u,v, pntsu,orderu,U, pntsv,orderv,V, P, nd, out, true, ucache);
+ float invw = 1/Skl(0,0)[3];
+ int outidx=0;
+ for (int nuv=0; nuv<=nd; nuv++) { // nuv = (# u derivs)+(#v derivs)
+ for (int nv=0; nv<=nuv; nv++) { // nv = #v derivs
+ int nu = nuv-nv;
+ int k=nu, l=nv; // k=(# u derivs) l=(# v derivs)
+ float *Akl = out[outidx].vec;
+ for (int i=1; i<=k; i++) {
+ float coeff = - BKE_nurb_binom_coeff(k, i) * Skl(i,0)[3];
+ madd_v4_v4fl(Akl, Skl(k-i,l), coeff);
+ }
+ for (int j=1; j<=l; j++) {
+ float coeff = - BKE_nurb_binom_coeff(l, j) * Skl(0,j)[3];
+ madd_v4_v4fl(Akl, Skl(k,l-j), coeff);
+ }
+ for (int i=1; i<=k; i++) {
+ for (int j=1; j<=l; j++) {
+ float coeff = -BKE_nurb_binom_coeff(k,i)*BKE_nurb_binom_coeff(l,j)*Skl(i,j)[3];
+ madd_v4_v4fl(Akl, Skl(k-i, l-j), coeff);
+ }
+ }
+ mul_v4_v4fl(Akl, Akl, invw);
+ outidx++;
+ }
+ }
} \ No newline at end of file
diff --git a/tests/interactive/curve_eval.h b/tests/interactive/curve_eval.h
index a7724839bc1..8dbe657b333 100644
--- a/tests/interactive/curve_eval.h
+++ b/tests/interactive/curve_eval.h
@@ -37,15 +37,27 @@ typedef struct BPoint {
float radius, pad; /* user-set radius per point for beveling etc */
} BPoint;
+/* Caches the value of basis functions evaluated at a given u coordinate
+ * so that a surface patch only has to evaluate once per row. We could do
+ * this with columns, too, but at a much worse space/time tradeoff.
+ */
+typedef struct BSplineCache {
+ float u;
+ int iu;
+ float Nu[NURBS_MAX_ORDER][NURBS_MAX_ORDER];
+} BSplineCacheU;
+
extern "C" {
void BKE_bspline_knot_calc(int flags, int pnts, int order, float knots[]);
int BKE_bspline_nz_basis_range(float u, float *knots, int num_pts, int order);
void BKE_bspline_basis_eval(float u, int i, float *U, int num_knots, int order, int nd, float out[][NURBS_MAX_ORDER]);
+ void BKE_bspline_curve_eval(float u, float *U, int num_pts, int order, BPoint *P, int stride, int nd, BPoint *out, bool premultiply_weight=false);
void BKE_nurbs_curve_eval(float u, float *U, int num_pts, int order, BPoint *P, int stride, int nd, BPoint *out);
void BKE_bspline_surf_eval(float u, float v,
int pntsu, int orderu, float *U,
int pntsv, int orderv, float *V,
- BPoint *P, int nd, BPoint *out);
+ BPoint *P, int nd, BPoint *out,
+ bool premultiply_weights=false, BSplineCacheU *ucache=NULL);
}
inline void madd_v4_v4fl(float r[4], const float a[4], float f)
diff --git a/tests/interactive/nurbs_derivative_eval.cpp b/tests/interactive/nurbs_derivative_eval.cpp
index 44a0f2e2447..b2dc39fce89 100644
--- a/tests/interactive/nurbs_derivative_eval.cpp
+++ b/tests/interactive/nurbs_derivative_eval.cpp
@@ -11,12 +11,12 @@
#include <string.h>
#include "curve_eval.h"
-/* Knots for basis function test */
-float knots[] = {0,0,0,0,1,1,1,1};
+/******* Test BSpline Basis Functions + first two derivatives ********/
+float knots[] = {0,0,0,0,.3,.6,1,1,1,1};
void test_basis() {
- int num_knots = 8;
- int order = 4;
+ int num_knots = 10;
+ int order = 3;
int p = order-1;
float out[NURBS_MAX_ORDER][NURBS_MAX_ORDER];
float umin=0, umax=1;
@@ -47,22 +47,45 @@ void test_basis() {
}
}
-/* Control points for surface test */
-float cpts[5][5][3] =
-{{{1,1,-0.7417486553512296},{1,2,-0.8272445659579368},{1,3,0.056384039811391506},{1,4,-0.8565668867842464},{1,5,-0.027038808836199912}},
-{{2,1,-0.8954639917925951},{2,2,0.7766849857222553},{2,3,-0.2762882340944248},{2,4,0.18616037830975074},{2,5,-0.8933549711042139}},
-{{3,1,-0.4470460035460979},{3,2,-0.9258719097096733},{3,3,-0.5237670863586921},{3,4,0.11854173291263326},{3,5,0.9615924014809489}},
-{{4,1,0.9195532263713426},{4,2,-0.10327619833646784},{4,3,-0.16756710093868232},{4,4,0.7063963753875271},{4,5,-0.05516995763136112}},
-{{5,1,0.9561682326127552},{5,2,-0.500642765940114},{5,3,0.2473747081580262},{5,4,0.10467945795748923},{5,5,0.5112014481491505}}};
+/******* Test BSpline Curves (values + first 2 derivatives) ********/
+float curveKnots[] = {0,0,0,.25,.5,.75,1,1,1};
+float curveCp[6][4] = {{-2.0, 0.0, 0.0, 1.0}, {0.0, 0.0, 0.0, 1.0}, {1.0, 0.0, 0.0, 1.0}, {2.0, 0.0, 1.3202035427093506, 1.0}, {0.9792511463165283, 0.014374732971191406, 1.8168606758117676, 9.309999465942383}, {-0.0020470619201660156, -0.3087310791015625, -0.42721521854400635, 1.0}};
+void test_bspline_curve() {
+ /* Put control polygon in BPoint format */
+ BPoint bp_cpts[25];
+ for (int u=0; u<6; u++) {
+ mul_v4_v4fl(bp_cpts[u].vec, &curveCp[u][0], 1.0);
+ }
+ /* Pass it to the evaluator */
+ FILE *of = fopen("/tmp/bspline_curve.txt","w");
+ double umin=0, umax=1; int nu=30;
+ int nd = 2; // Maximum derivative to evaluate
+ fprintf(of, "crv={");
+ for (int i=0; i<nu; i++) {
+ float u = umin + (umax-umin)/(nu-1)*i;
+ BPoint out[6];
+ BKE_bspline_curve_eval(u, curveKnots, 6, 3, bp_cpts, 1, nd, out);
+ fprintf(of, "{");
+ for (int d=0; d<nd; d++) {
+ fprintf(of,(d==nd-1)?"%f,%f,%f":"%f,%f,%f,",out[d].vec[0],out[d].vec[1],out[d].vec[2]);
+ }
+ fprintf(of,(i==nu-1)?"}};":"},\n");
+ }
+ fclose(of);
+}
+
+/******* Test BSpline Surfaces (values + first 2 derivatives) ********/
+float surfCp[5][5][4] =
+{{{1,1,-0.7417486553512296,1},{1,2,-0.8272445659579368,1},{1,3,0.056384039811391506,1},{1,4,-0.8565668867842464,1},{1,5,-0.027038808836199912,1}},{{2,1,-0.8954639917925951,1},{2,2,0.7766849857222553,1},{2,3,-0.2762882340944248,1},{2,4,0.18616037830975074,1},{2,5,-0.8933549711042139,1}},{{3,1,-0.4470460035460979,1},{3,2,-0.9258719097096733,1},{3,3,-0.5237670863586921,10},{3,4,0.11854173291263326,1},{3,5,0.9615924014809489,1}},{{4,1,0.9195532263713426,1},{4,2,-0.10327619833646784,1},{4,3,-0.16756710093868232,1},{4,4,0.7063963753875271,1},{4,5,-0.05516995763136112,1}},{{5,1,0.9561682326127552,1},{5,2,-0.500642765940114,1},{5,3,0.2473747081580262,1},{5,4,0.10467945795748923,1},{5,5,0.5112014481491505,1}}};
float surfU[] = {0,0,0,0,.5,1,1,1,1};
float surfV[] = {0,0,0,0,.5,1,1,1,1};
-void test_surf() {
+void test_bspline_surf() {
/* Put control mesh in BPoint format */
BPoint bp_cpts[25];
for (int u=0; u<5; u++) {
for (int v=0; v<5; v++) {
- mul_v4_v4fl(bp_cpts[5*v+u].vec, &cpts[u][v][0], 1.0);
+ mul_v4_v4fl(bp_cpts[5*v+u].vec, &surfCp[u][v][0], 1.0);
bp_cpts[5*v+u].vec[3] = 1.0;
}
}
@@ -91,10 +114,37 @@ void test_surf() {
fclose(of);
}
+/******* Test NURBS Curves (values + first 2 derivatives) ********/
+void test_nurbs_curve() {
+ /* Put control polygon in BPoint format */
+ BPoint bp_cpts[25];
+ for (int u=0; u<6; u++) {
+ mul_v4_v4fl(bp_cpts[u].vec, &curveCp[u][0], 1.0);
+ }
+ /* Pass it to the evaluator */
+ FILE *of = fopen("/tmp/nurbs_curve.txt","w");
+ double umin=0, umax=1; int nu=30;
+ int nd = 2; // Maximum derivative to evaluate
+ fprintf(of, "crv={");
+ for (int i=0; i<nu; i++) {
+ float u = umin + (umax-umin)/(nu-1)*i;
+ BPoint out[6];
+ BKE_nurbs_curve_eval(u, curveKnots, 6, 3, bp_cpts, 1, nd, out);
+ fprintf(of, "{");
+ for (int d=0; d<nd; d++) {
+ fprintf(of,(d==nd-1)?"%f,%f,%f":"%f,%f,%f,",out[d].vec[0],out[d].vec[1],out[d].vec[2]);
+ }
+ fprintf(of,(i==nu-1)?"}};":"},\n");
+ }
+ fclose(of);
+}
+
int main(int argc, const char * argv[])
{
test_basis();
- test_surf();
+ test_bspline_surf();
+ test_bspline_curve();
+ test_nurbs_curve();
return 0;
}
diff --git a/tests/interactive/nurbs_eval.nb b/tests/interactive/nurbs_eval.nb
index 163ccd4f3f6..232ba3f7db2 100644
--- a/tests/interactive/nurbs_eval.nb
+++ b/tests/interactive/nurbs_eval.nb
@@ -10,10 +10,10 @@
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 157, 7]
-NotebookDataLength[ 254953, 4758]
-NotebookOptionsPosition[ 254004, 4719]
-NotebookOutlinePosition[ 254364, 4735]
-CellTagsIndexPosition[ 254321, 4732]
+NotebookDataLength[ 286606, 5445]
+NotebookOptionsPosition[ 285402, 5398]
+NotebookOutlinePosition[ 285762, 5414]
+CellTagsIndexPosition[ 285719, 5411]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
@@ -25,23 +25,203 @@ Cell["NURBS Curve", "Section",
Cell[CellGroupData[{
-Cell[BoxData[
- RowBox[{"Table", "[",
- RowBox[{
- RowBox[{"Random", "[", "]"}], ",",
+Cell[BoxData[{
+ RowBox[{
+ RowBox[{"curveKnots", "=",
RowBox[{"{",
- RowBox[{"i", ",", "10"}], "}"}]}], "]"}]], "Input",
- CellChangeTimes->{{3.6152391992093897`*^9, 3.615239210773265*^9}}],
+ RowBox[{
+ "0", ",", "0", ",", "0", ",", ".25", ",", ".5", ",", ".75", ",", "1", ",",
+ "1", ",", "1"}], "}"}]}], ";"}], "\[IndentingNewLine]",
+ RowBox[{
+ RowBox[{"curveCp", "=",
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{
+ RowBox[{"-", "2.0"}], ",", "0.0", ",", "0.0", ",", "1.0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"0.0", ",", "0.0", ",", "0.0", ",", "1.0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"1.0", ",", "0.0", ",", "0.0", ",", "1.0"}], "}"}], ",",
+ RowBox[{"{",
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generated by cgit v1.2.3 (git 2.25.1) at 2024-05-22 19:43:25 +0300