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/*
* Copyright 2017 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "GrCCCubicShader.h"
#include "glsl/GrGLSLFragmentShaderBuilder.h"
#include "glsl/GrGLSLProgramBuilder.h"
#include "glsl/GrGLSLVertexGeoBuilder.h"
using Shader = GrCCCoverageProcessor::Shader;
void GrCCCubicShader::emitSetupCode(GrGLSLVertexGeoBuilder* s, const char* pts,
const char* wind, const char** /*outHull4*/) const {
// Find the cubic's power basis coefficients.
s->codeAppendf("float2x4 C = float4x4(-1, 3, -3, 1, "
" 3, -6, 3, 0, "
"-3, 3, 0, 0, "
" 1, 0, 0, 0) * transpose(%s);", pts);
// Find the cubic's inflection function.
s->codeAppend ("float D3 = +determinant(float2x2(C[0].yz, C[1].yz));");
s->codeAppend ("float D2 = -determinant(float2x2(C[0].xz, C[1].xz));");
s->codeAppend ("float D1 = +determinant(float2x2(C));");
// Shift the exponents in D so the largest magnitude falls somewhere in 1..2. This protects us
// from overflow while solving for roots and KLM functionals.
s->codeAppend ("float Dmax = max(max(abs(D1), abs(D2)), abs(D3));");
s->codeAppend ("float norm;");
if (s->getProgramBuilder()->shaderCaps()->fpManipulationSupport()) {
s->codeAppend ("int exp;");
s->codeAppend ("frexp(Dmax, exp);");
s->codeAppend ("norm = ldexp(1, 1 - exp);");
} else {
s->codeAppend ("norm = 1/Dmax;"); // Dmax will not be 0 because we cull line cubics on CPU.
}
s->codeAppend ("D3 *= norm;");
s->codeAppend ("D2 *= norm;");
s->codeAppend ("D1 *= norm;");
// Calculate the KLM matrix.
s->declareGlobal(fKLMMatrix);
s->codeAppend ("float discr = 3*D2*D2 - 4*D1*D3;");
s->codeAppend ("float x = discr >= 0 ? 3 : 1;");
s->codeAppend ("float q = sqrt(x * abs(discr));");
s->codeAppend ("q = x*D2 + (D2 >= 0 ? q : -q);");
s->codeAppend ("float2 l, m;");
s->codeAppend ("l.ts = float2(q, 2*x * D1);");
s->codeAppend ("m.ts = float2(2, q) * (discr >= 0 ? float2(D3, 1) "
": float2(D2*D2 - D3*D1, D1));");
s->codeAppend ("float4 K;");
s->codeAppend ("float4 lm = l.sstt * m.stst;");
s->codeAppend ("K = float4(0, lm.x, -lm.y - lm.z, lm.w);");
s->codeAppend ("float4 L, M;");
s->codeAppend ("lm.yz += 2*lm.zy;");
s->codeAppend ("L = float4(-1,x,-x,1) * l.sstt * (discr >= 0 ? l.ssst * l.sttt : lm);");
s->codeAppend ("M = float4(-1,x,-x,1) * m.sstt * (discr >= 0 ? m.ssst * m.sttt : lm.xzyw);");
s->codeAppend ("int middlerow = abs(D2) > abs(D1) ? 2 : 1;");
s->codeAppend ("float3x3 CI = inverse(float3x3(C[0][0], C[0][middlerow], C[0][3], "
"C[1][0], C[1][middlerow], C[1][3], "
" 0, 0, 1));");
s->codeAppendf("%s = CI * float3x3(K[0], K[middlerow], K[3], "
"L[0], L[middlerow], L[3], "
"M[0], M[middlerow], M[3]);", fKLMMatrix.c_str());
// Evaluate the cubic at T=.5 for a mid-ish point.
s->codeAppendf("float2 midpoint = %s * float4(.125, .375, .375, .125);", pts);
// Orient the KLM matrix so L & M are both positive on the side of the curve we wish to fill.
s->codeAppendf("float2 orientation = sign(float3(midpoint, 1) * float2x3(%s[1], %s[2]));",
fKLMMatrix.c_str(), fKLMMatrix.c_str());
s->codeAppendf("%s *= float3x3(orientation[0] * orientation[1], 0, 0, "
"0, orientation[0], 0, "
"0, 0, orientation[1]);", fKLMMatrix.c_str());
// Determine the amount of additional coverage to subtract out for the flat edge (P3 -> P0).
s->declareGlobal(fEdgeDistanceEquation);
s->codeAppendf("int edgeidx0 = %s > 0 ? 3 : 0;", wind);
s->codeAppendf("float2 edgept0 = %s[edgeidx0];", pts);
s->codeAppendf("float2 edgept1 = %s[3 - edgeidx0];", pts);
Shader::EmitEdgeDistanceEquation(s, "edgept0", "edgept1", fEdgeDistanceEquation.c_str());
}
void GrCCCubicShader::onEmitVaryings(GrGLSLVaryingHandler* varyingHandler,
GrGLSLVarying::Scope scope, SkString* code,
const char* position, const char* coverage,
const char* cornerCoverage) {
fKLM_fEdge.reset(kFloat4_GrSLType, scope);
varyingHandler->addVarying("klm_and_edge", &fKLM_fEdge);
code->appendf("float3 klm = float3(%s, 1) * %s;", position, fKLMMatrix.c_str());
// We give L & M both the same sign as wind, in order to pass this value to the fragment shader.
// (Cubics are pre-chopped such that L & M do not change sign within any individual segment.)
code->appendf("%s.xyz = klm * float3(1, %s, %s);",
OutName(fKLM_fEdge), coverage, coverage); // coverage == wind on curves.
code->appendf("%s.w = dot(float3(%s, 1), %s);", // Flat edge opposite the curve.
OutName(fKLM_fEdge), position, fEdgeDistanceEquation.c_str());
fGradMatrix.reset(kFloat4_GrSLType, scope);
varyingHandler->addVarying("grad_matrix", &fGradMatrix);
code->appendf("%s.xy = 2*bloat * 3 * klm[0] * %s[0].xy;",
OutName(fGradMatrix), fKLMMatrix.c_str());
code->appendf("%s.zw = -2*bloat * (klm[1] * %s[2].xy + klm[2] * %s[1].xy);",
OutName(fGradMatrix), fKLMMatrix.c_str(), fKLMMatrix.c_str());
if (cornerCoverage) {
code->appendf("half hull_coverage; {");
this->calcHullCoverage(code, OutName(fKLM_fEdge), OutName(fGradMatrix), "hull_coverage");
code->appendf("}");
fCornerCoverage.reset(kHalf2_GrSLType, scope);
varyingHandler->addVarying("corner_coverage", &fCornerCoverage);
code->appendf("%s = half2(hull_coverage, 1) * %s;",
OutName(fCornerCoverage), cornerCoverage);
}
}
void GrCCCubicShader::onEmitFragmentCode(GrGLSLFPFragmentBuilder* f,
const char* outputCoverage) const {
this->calcHullCoverage(&AccessCodeString(f), fKLM_fEdge.fsIn(), fGradMatrix.fsIn(),
outputCoverage);
// Wind is the sign of both L and/or M. Take the sign of whichever has the larger magnitude.
// (In reality, either would be fine because we chop cubics with more than a half pixel of
// padding around the L & M lines, so neither should approach zero.)
f->codeAppend ("half wind = sign(l + m);");
f->codeAppendf("%s *= wind;", outputCoverage);
if (fCornerCoverage.fsIn()) {
f->codeAppendf("%s = %s.x * %s.y + %s;", // Attenuated corner coverage.
outputCoverage, fCornerCoverage.fsIn(), fCornerCoverage.fsIn(),
outputCoverage);
}
}
void GrCCCubicShader::calcHullCoverage(SkString* code, const char* klmAndEdge,
const char* gradMatrix, const char* outputCoverage) const {
code->appendf("float k = %s.x, l = %s.y, m = %s.z;", klmAndEdge, klmAndEdge, klmAndEdge);
code->append ("float f = k*k*k - l*m;");
code->appendf("float2 grad = %s.xy * k + %s.zw;", gradMatrix, gradMatrix);
code->append ("float fwidth = abs(grad.x) + abs(grad.y);");
code->appendf("%s = min(0.5 - f/fwidth, 1);", outputCoverage); // Curve coverage.
code->appendf("half d = min(%s.w, 0);", klmAndEdge); // Flat edge opposite the curve.
code->appendf("%s = max(%s + d, 0);", outputCoverage, outputCoverage); // Total hull coverage.
}
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