blender/intern/cycles/subd/subd_patch.cpp

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/*
* Copyright 2011, Blender Foundation.
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/* Parts adapted from code in the public domain in NVidia Mesh Tools. */
#include "mesh.h"
#include "subd_patch.h"
#include "util_math.h"
#include "util_types.h"
CCL_NAMESPACE_BEGIN
/* De Casteljau Evaluation */
static float3 decasteljau_quadratic(float t, const float3 cp[3])
{
float3 d0 = cp[0] + t*(cp[1] - cp[0]);
float3 d1 = cp[1] + t*(cp[2] - cp[1]);
return d0 + t*(d1 - d0);
}
static void decasteljau_cubic(float3 *P, float3 *dt, float t, const float3 cp[4])
{
float3 d0 = cp[0] + t*(cp[1] - cp[0]);
float3 d1 = cp[1] + t*(cp[2] - cp[1]);
float3 d2 = cp[2] + t*(cp[3] - cp[2]);
d0 += t*(d1 - d0);
d1 += t*(d2 - d1);
*P = d0 + t*(d1 - d0);
if(dt) *dt = d1 - d0;
}
static void decasteljau_bicubic(float3 *P, float3 *du, float3 *dv, const float3 cp[16], float u, float v)
{
float3 ucp[4], utn[4];
/* interpolate over u */
decasteljau_cubic(ucp+0, utn+0, u, cp);
decasteljau_cubic(ucp+1, utn+1, u, cp+4);
decasteljau_cubic(ucp+2, utn+2, u, cp+8);
decasteljau_cubic(ucp+3, utn+3, u, cp+12);
/* interpolate over v */
decasteljau_cubic(P, dv, v, ucp);
if(du) decasteljau_cubic(du, NULL, v, utn);
}
static float3 decasteljau_tangent(const float3 cp[12], float u, float v)
{
float3 ucp[3];
decasteljau_cubic(ucp+0, NULL, v, cp);
decasteljau_cubic(ucp+1, NULL, v, cp+4);
decasteljau_cubic(ucp+2, NULL, v, cp+8);
return decasteljau_quadratic(u, ucp);
}
/* Linear Quad Patch */
void LinearQuadPatch::eval(float3 *P, float3 *dPdu, float3 *dPdv, float u, float v)
{
float3 d0 = interp(hull[0], hull[1], u);
float3 d1 = interp(hull[2], hull[3], u);
*P = interp(d0, d1, v);
if(dPdu && dPdv) {
*dPdu = interp(hull[1] - hull[0], hull[3] - hull[2], v);
*dPdv = interp(hull[2] - hull[0], hull[3] - hull[1], u);
}
}
BoundBox LinearQuadPatch::bound()
{
BoundBox bbox;
for(int i = 0; i < 4; i++)
bbox.grow(hull[i]);
return bbox;
}
/* Linear Triangle Patch */
void LinearTrianglePatch::eval(float3 *P, float3 *dPdu, float3 *dPdv, float u, float v)
{
*P = u*hull[0] + v*hull[1] + (1.0f - u - v)*hull[2];
if(dPdu && dPdv) {
*dPdu = hull[0] - hull[2];
*dPdv = hull[1] - hull[2];
}
}
BoundBox LinearTrianglePatch::bound()
{
BoundBox bbox;
for(int i = 0; i < 3; i++)
bbox.grow(hull[i]);
return bbox;
}
/* Bicubic Patch */
void BicubicPatch::eval(float3 *P, float3 *dPdu, float3 *dPdv, float u, float v)
{
decasteljau_bicubic(P, dPdu, dPdv, hull, u, v);
}
BoundBox BicubicPatch::bound()
{
BoundBox bbox;
for(int i = 0; i < 16; i++)
bbox.grow(hull[i]);
return bbox;
}
/* Bicubic Patch with Tangent Fields */
void BicubicTangentPatch::eval(float3 *P, float3 *dPdu, float3 *dPdv, float u, float v)
{
decasteljau_bicubic(P, NULL, NULL, hull, u, v);
if(dPdu) *dPdu = decasteljau_tangent(utan, u, v);
if(dPdv) *dPdv = decasteljau_tangent(vtan, v, u);
}
BoundBox BicubicTangentPatch::bound()
{
BoundBox bbox;
for(int i = 0; i < 16; i++)
bbox.grow(hull[i]);
return bbox;
}
/* Gregory Patch */
static float no_zero_div(float f)
{
if(f == 0.0f) return 1.0f;
return f;
}
void GregoryQuadPatch::eval(float3 *P, float3 *dPdu, float3 *dPdv, float u, float v)
{
float3 bicubic[16];
float U = 1 - u;
float V = 1 - v;
/* 8 9 10 11
* 12 0\1 2/3 13
* 14 4/5 6\7 15
* 16 17 18 19
*/
bicubic[5] = (u*hull[1] + v*hull[0])/no_zero_div(u + v);
bicubic[6] = (U*hull[2] + v*hull[3])/no_zero_div(U + v);
bicubic[9] = (u*hull[5] + V*hull[4])/no_zero_div(u + V);
bicubic[10] = (U*hull[6] + V*hull[7])/no_zero_div(U + V);
// Map gregory control points to bezier control points.
bicubic[0] = hull[8];
bicubic[1] = hull[9];
bicubic[2] = hull[10];
bicubic[3] = hull[11];
bicubic[4] = hull[12];
bicubic[7] = hull[13];
bicubic[8] = hull[14];
bicubic[11] = hull[15];
bicubic[12] = hull[16];
bicubic[13] = hull[17];
bicubic[14] = hull[18];
bicubic[15] = hull[19];
decasteljau_bicubic(P, dPdu, dPdv, bicubic, u, v);
}
BoundBox GregoryQuadPatch::bound()
{
BoundBox bbox;
for(int i = 0; i < 20; i++)
bbox.grow(hull[i]);
return bbox;
}
void GregoryTrianglePatch::eval(float3 *P, float3 *dPdu, float3 *dPdv, float u, float v)
{
/* 6
*
* 14 0/1 7
*
* 13 5/4 3\2 8
*
* 12 11 10 9
*/
float w = 1 - u - v;
float uu = u * u;
float vv = v * v;
float ww = w * w;
float uuu = uu * u;
float vvv = vv * v;
float www = ww * w;
float U = 1 - u;
float V = 1 - v;
float W = 1 - w;
float3 C0 = ( v*U * hull[5] + u*V * hull[4] ) / no_zero_div(v*U + u*V);
float3 C1 = ( w*V * hull[3] + v*W * hull[2] ) / no_zero_div(w*V + v*W);
float3 C2 = ( u*W * hull[1] + w*U * hull[0] ) / no_zero_div(u*W + w*U);
*P =
(hull[12] * www + 3*hull[11] * ww*u + 3*hull[10] * w*uu + hull[ 9]*uuu) * (w + u) +
(hull[ 9] * uuu + 3*hull[ 8] * uu*v + 3*hull[ 7] * u*vv + hull[ 6]*vvv) * (u + v) +
(hull[ 6] * vvv + 3*hull[14] * vv*w + 3*hull[13] * v*ww + hull[12]*www) * (v + w) -
(hull[12] * www*w + hull[ 9] * uuu*u + hull[ 6] * vvv*v) +
12*(C0 * u*v*ww + C1 * uu*v*w + C2 * u*vv*w);
if(dPdu || dPdv) {
float3 E1 = (hull[12]*www + 3*hull[11]*ww*u + 3*hull[10]*w*uu + hull[ 9]*uuu);
float3 E2 = (hull[ 9]*uuu + 3*hull[ 8]*uu*v + 3*hull[ 7]*u*vv + hull[ 6]*vvv);
float3 E3 = (hull[ 6]*vvv + 3*hull[14]*vv*w + 3*hull[13]*v*ww + hull[12]*www);
if(dPdu) {
float3 E1u = 3*( - hull[12]*ww + hull[11]*(ww-2*u*w) + hull[10]*(2*u*w-uu) + hull[ 9]*uu);
float3 E2u = 3*( hull[ 9]*uu + 2*hull[ 8]*u*v + hull[ 7]*vv );
float3 E3u = 3*( - hull[14]*vv - 2*hull[13]*v*w - hull[12]*ww);
float3 Su = 4*( -hull[12]*www + hull[9]*uuu);
float3 Cu = 12*( C0*(ww*v-2*u*v*w) + C1*(2*u*v*w-uu*v) + C2*vv*(w-u) );
*dPdu = E1u*(w+u) + (E2+E2u*(u+v)) + (E3u*(v+w)-E3) - Su + Cu;
}
if(dPdv) {
float3 E1v = 3*(-hull[12]*ww - 2*hull[11]*w*u - hull[10]*uu );
float3 E2v = 3*( hull[ 8]*uu + 2*hull[ 7]*u*v + hull[ 6]*vv);
float3 E3v = 3*( hull[ 6]*vv + hull[14]*(2*w*v-vv) + hull[13]*(ww-2*w*v) - hull[12]*ww);
float3 Sv = 4*(-hull[12]*www + hull[ 6]*vvv);
float3 Cv = 12*(C0*(u*ww-2*u*v*w) + C1*uu*(w-v) + C2*(2*u*v*w-u*vv));
*dPdv = ((E1v*(w+u)-E1) + (E2+E2v*(u+v)) + E3v*(v+w) - Sv + Cv );
}
}
}
BoundBox GregoryTrianglePatch::bound()
{
BoundBox bbox;
for(int i = 0; i < 20; i++)
bbox.grow(hull[i]);
return bbox;
}
CCL_NAMESPACE_END