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skia/skia.git/847d55be4e6273fc3cd9c0b30c7bfc8a2d6575b7/./src/gpu/ccpr/GrCCFillGeometry.cpp
blob: 81692cfb689a63faacc252cc3ad0b57d51988c07 [file]
/*
* 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 "GrCCFillGeometry.h"
#include "GrTypes.h"
#include "SkGeometry.h"
#include <algorithm>
#include <cmath>
#include <cstdlib>
static constexpr float kFlatnessThreshold = 1/16.f; // 1/16 of a pixel.
void GrCCFillGeometry::beginPath() {
SkASSERT(!fBuildingContour);
fVerbs.push_back(Verb::kBeginPath);
}
void GrCCFillGeometry::beginContour(const SkPoint& pt) {
SkASSERT(!fBuildingContour);
// Store the current verb count in the fTriangles field for now. When we close the contour we
// will use this value to calculate the actual number of triangles in its fan.
fCurrContourTallies = {fVerbs.count(), 0, 0, 0, 0};
fPoints.push_back(pt);
fVerbs.push_back(Verb::kBeginContour);
fCurrAnchorPoint = pt;
SkDEBUGCODE(fBuildingContour = true);
}
void GrCCFillGeometry::lineTo(const SkPoint P[2]) {
SkASSERT(fBuildingContour);
SkASSERT(P[0] == fPoints.back());
Sk2f p0 = Sk2f::Load(P);
Sk2f p1 = Sk2f::Load(P+1);
this->appendLine(p0, p1);
}
inline void GrCCFillGeometry::appendLine(const Sk2f& p0, const Sk2f& p1) {
SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1]));
if ((p0 == p1).allTrue()) {
return;
}
p1.store(&fPoints.push_back());
fVerbs.push_back(Verb::kLineTo);
}
static inline Sk2f normalize(const Sk2f& n) {
Sk2f nn = n*n;
return n * (nn + SkNx_shuffle<1,0>(nn)).rsqrt();
}
static inline float dot(const Sk2f& a, const Sk2f& b) {
float product[2];
(a * b).store(product);
return product[0] + product[1];
}
static inline bool are_collinear(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2,
float tolerance = kFlatnessThreshold) {
Sk2f l = p2 - p0; // Line from p0 -> p2.
// lwidth = Manhattan width of l.
Sk2f labs = l.abs();
float lwidth = labs[0] + labs[1];
// d = |p1 - p0| dot | l.y|
// |-l.x| = distance from p1 to l.
Sk2f dd = (p1 - p0) * SkNx_shuffle<1,0>(l);
float d = dd[0] - dd[1];
// We are collinear if a box with radius "tolerance", centered on p1, touches the line l.
// To decide this, we check if the distance from p1 to the line is less than the distance from
// p1 to the far corner of this imaginary box, along that same normal vector.
// The far corner of the box can be found at "p1 + sign(n) * tolerance", where n is normal to l:
//
// abs(dot(p1 - p0, n)) <= dot(sign(n) * tolerance, n)
//
// Which reduces to:
//
// abs(d) <= (n.x * sign(n.x) + n.y * sign(n.y)) * tolerance
// abs(d) <= (abs(n.x) + abs(n.y)) * tolerance
//
// Use "<=" in case l == 0.
return std::abs(d) <= lwidth * tolerance;
}
static inline bool are_collinear(const SkPoint P[4], float tolerance = kFlatnessThreshold) {
Sk4f Px, Py; // |Px Py| |p0 - p3|
Sk4f::Load2(P, &Px, &Py); // |. . | = |p1 - p3|
Px -= Px[3]; // |. . | |p2 - p3|
Py -= Py[3]; // |. . | | 0 |
// Find [lx, ly] = the line from p3 to the furthest-away point from p3.
Sk4f Pwidth = Px.abs() + Py.abs(); // Pwidth = Manhattan width of each point.
int lidx = Pwidth[0] > Pwidth[1] ? 0 : 1;
lidx = Pwidth[lidx] > Pwidth[2] ? lidx : 2;
float lx = Px[lidx], ly = Py[lidx];
float lwidth = Pwidth[lidx]; // lwidth = Manhattan width of [lx, ly].
// |Px Py|
// d = |. . | * | ly| = distances from each point to l (two of the distances will be zero).
// |. . | |-lx|
// |. . |
Sk4f d = Px*ly - Py*lx;
// We are collinear if boxes with radius "tolerance", centered on all 4 points all touch line l.
// (See the rationale for this formula in the above, 3-point version of this function.)
// Use "<=" in case l == 0.
return (d.abs() <= lwidth * tolerance).allTrue();
}
// Returns whether the (convex) curve segment is monotonic with respect to [endPt - startPt].
static inline bool is_convex_curve_monotonic(const Sk2f& startPt, const Sk2f& tan0,
const Sk2f& endPt, const Sk2f& tan1) {
Sk2f v = endPt - startPt;
float dot0 = dot(tan0, v);
float dot1 = dot(tan1, v);
// A small, negative tolerance handles floating-point error in the case when one tangent
// approaches 0 length, meaning the (convex) curve segment is effectively a flat line.
float tolerance = -std::max(std::abs(dot0), std::abs(dot1)) * SK_ScalarNearlyZero;
return dot0 >= tolerance && dot1 >= tolerance;
}
template<int N> static inline SkNx<N,float> lerp(const SkNx<N,float>& a, const SkNx<N,float>& b,
const SkNx<N,float>& t) {
return SkNx_fma(t, b - a, a);
}
void GrCCFillGeometry::quadraticTo(const SkPoint P[3]) {
SkASSERT(fBuildingContour);
SkASSERT(P[0] == fPoints.back());
Sk2f p0 = Sk2f::Load(P);
Sk2f p1 = Sk2f::Load(P+1);
Sk2f p2 = Sk2f::Load(P+2);
// Don't crunch on the curve if it is nearly flat (or just very small). Flat curves can break
// The monotonic chopping math.
if (are_collinear(p0, p1, p2)) {
this->appendLine(p0, p2);
return;
}
this->appendQuadratics(p0, p1, p2);
}
inline void GrCCFillGeometry::appendQuadratics(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2) {
Sk2f tan0 = p1 - p0;
Sk2f tan1 = p2 - p1;
// This should almost always be this case for well-behaved curves in the real world.
if (is_convex_curve_monotonic(p0, tan0, p2, tan1)) {
this->appendMonotonicQuadratic(p0, p1, p2);
return;
}
// Chop the curve into two segments with equal curvature. To do this we find the T value whose
// tangent angle is halfway between tan0 and tan1.
Sk2f n = normalize(tan0) - normalize(tan1);
// The midtangent can be found where (dQ(t) dot n) = 0:
//
// 0 = (dQ(t) dot n) = | 2*t 1 | * | p0 - 2*p1 + p2 | * | n |
// | -2*p0 + 2*p1 | | . |
//
// = | 2*t 1 | * | tan1 - tan0 | * | n |
// | 2*tan0 | | . |
//
// = 2*t * ((tan1 - tan0) dot n) + (2*tan0 dot n)
//
// t = (tan0 dot n) / ((tan0 - tan1) dot n)
Sk2f dQ1n = (tan0 - tan1) * n;
Sk2f dQ0n = tan0 * n;
Sk2f t = (dQ0n + SkNx_shuffle<1,0>(dQ0n)) / (dQ1n + SkNx_shuffle<1,0>(dQ1n));
t = Sk2f::Min(Sk2f::Max(t, 0), 1); // Clamp for FP error.
Sk2f p01 = SkNx_fma(t, tan0, p0);
Sk2f p12 = SkNx_fma(t, tan1, p1);
Sk2f p012 = lerp(p01, p12, t);
this->appendMonotonicQuadratic(p0, p01, p012);
this->appendMonotonicQuadratic(p012, p12, p2);
}
inline void GrCCFillGeometry::appendMonotonicQuadratic(const Sk2f& p0, const Sk2f& p1,
const Sk2f& p2) {
// Don't send curves to the GPU if we know they are nearly flat (or just very small).
if (are_collinear(p0, p1, p2)) {
this->appendLine(p0, p2);
return;
}
SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1]));
SkASSERT((p0 != p2).anyTrue());
p1.store(&fPoints.push_back());
p2.store(&fPoints.push_back());
fVerbs.push_back(Verb::kMonotonicQuadraticTo);
++fCurrContourTallies.fQuadratics;
}
static inline Sk2f first_unless_nearly_zero(const Sk2f& a, const Sk2f& b) {
Sk2f aa = a*a;
aa += SkNx_shuffle<1,0>(aa);
SkASSERT(aa[0] == aa[1]);
Sk2f bb = b*b;
bb += SkNx_shuffle<1,0>(bb);
SkASSERT(bb[0] == bb[1]);
return (aa > bb * SK_ScalarNearlyZero).thenElse(a, b);
}
static inline void get_cubic_tangents(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2,
const Sk2f& p3, Sk2f* tan0, Sk2f* tan1) {
*tan0 = first_unless_nearly_zero(p1 - p0, p2 - p0);
*tan1 = first_unless_nearly_zero(p3 - p2, p3 - p1);
}
static inline bool is_cubic_nearly_quadratic(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2,
const Sk2f& p3, const Sk2f& tan0, const Sk2f& tan1,
Sk2f* c) {
Sk2f c1 = SkNx_fma(Sk2f(1.5f), tan0, p0);
Sk2f c2 = SkNx_fma(Sk2f(-1.5f), tan1, p3);
*c = (c1 + c2) * .5f; // Hopefully optimized out if not used?
return ((c1 - c2).abs() <= 1).allTrue();
}
enum class ExcludedTerm : bool {
kQuadraticTerm,
kLinearTerm
};
// Finds where to chop a non-loop around its inflection points. The resulting cubic segments will be
// chopped such that a box of radius 'padRadius', centered at any point along the curve segment, is
// guaranteed to not cross the tangent lines at the inflection points (a.k.a lines L & M).
//
// 'chops' will be filled with 0, 2, or 4 T values. The segments between T0..T1 and T2..T3 must be
// drawn with flat lines instead of cubics.
//
// A serpentine cubic has two inflection points, so this method takes Sk2f and computes the padding
// for both in SIMD.
static inline void find_chops_around_inflection_points(float padRadius, Sk2f tl, Sk2f sl,
const Sk2f& C0, const Sk2f& C1,
ExcludedTerm skipTerm, float Cdet,
SkSTArray<4, float>* chops) {
SkASSERT(chops->empty());
SkASSERT(padRadius >= 0);
padRadius /= std::abs(Cdet); // Scale this single value rather than all of C^-1 later on.
// The homogeneous parametric functions for distance from lines L & M are:
//
// l(t,s) = (t*sl - s*tl)^3
// m(t,s) = (t*sm - s*tm)^3
//
// See "Resolution Independent Curve Rendering using Programmable Graphics Hardware",
// 4.3 Finding klmn:
//
// https://www.microsoft.com/en-us/research/wp-content/uploads/2005/01/p1000-loop.pdf
//
// From here on we use Sk2f with "L" names, but the second lane will be for line M.
tl = (sl > 0).thenElse(tl, -tl); // Tl=tl/sl is the triple root of l(t,s). Normalize so s >= 0.
sl = sl.abs();
// Convert l(t,s), m(t,s) to power-basis form:
//
// | l3 m3 |
// |l(t,s) m(t,s)| = |t^3 t^2*s t*s^2 s^3| * | l2 m2 |
// | l1 m1 |
// | l0 m0 |
//
Sk2f l3 = sl*sl*sl;
Sk2f l2or1 = (ExcludedTerm::kLinearTerm == skipTerm) ? sl*sl*tl*-3 : sl*tl*tl*3;
// The equation for line L can be found as follows:
//
// L = C^-1 * (l excluding skipTerm)
//
// (See comments for GrPathUtils::calcCubicInverseTransposePowerBasisMatrix.)
// We are only interested in the normal to L, so only need the upper 2x2 of C^-1. And rather
// than divide by determinant(C) here, we have already performed this divide on padRadius.
Sk2f Lx = C1[1]*l3 - C0[1]*l2or1;
Sk2f Ly = -C1[0]*l3 + C0[0]*l2or1;
// A box of radius "padRadius" is touching line L if "center dot L" is less than the Manhattan
// with of L. (See rationale in are_collinear.)
Sk2f Lwidth = Lx.abs() + Ly.abs();
Sk2f pad = Lwidth * padRadius;
// Will T=(t + cbrt(pad))/s be greater than 0? No need to solve roots outside T=0..1.
Sk2f insideLeftPad = pad + tl*tl*tl;
// Will T=(t - cbrt(pad))/s be less than 1? No need to solve roots outside T=0..1.
Sk2f tms = tl - sl;
Sk2f insideRightPad = pad - tms*tms*tms;
// Solve for the T values where abs(l(T)) = pad.
if (insideLeftPad[0] > 0 && insideRightPad[0] > 0) {
float padT = cbrtf(pad[0]);
Sk2f pts = (tl[0] + Sk2f(-padT, +padT)) / sl[0];
pts.store(chops->push_back_n(2));
}
// Solve for the T values where abs(m(T)) = pad.
if (insideLeftPad[1] > 0 && insideRightPad[1] > 0) {
float padT = cbrtf(pad[1]);
Sk2f pts = (tl[1] + Sk2f(-padT, +padT)) / sl[1];
pts.store(chops->push_back_n(2));
}
}
static inline void swap_if_greater(float& a, float& b) {
if (a > b) {
std::swap(a, b);
}
}
// Finds where to chop a non-loop around its intersection point. The resulting cubic segments will
// be chopped such that a box of radius 'padRadius', centered at any point along the curve segment,
// is guaranteed to not cross the tangent lines at the intersection point (a.k.a lines L & M).
//
// 'chops' will be filled with 0, 2, or 4 T values. The segments between T0..T1 and T2..T3 must be
// drawn with quadratic splines instead of cubics.
//
// A loop intersection falls at two different T values, so this method takes Sk2f and computes the
// padding for both in SIMD.
static inline void find_chops_around_loop_intersection(float padRadius, Sk2f t2, Sk2f s2,
const Sk2f& C0, const Sk2f& C1,
ExcludedTerm skipTerm, float Cdet,
SkSTArray<4, float>* chops) {
SkASSERT(chops->empty());
SkASSERT(padRadius >= 0);
padRadius /= std::abs(Cdet); // Scale this single value rather than all of C^-1 later on.
// The parametric functions for distance from lines L & M are:
//
// l(T) = (T - Td)^2 * (T - Te)
// m(T) = (T - Td) * (T - Te)^2
//
// See "Resolution Independent Curve Rendering using Programmable Graphics Hardware",
// 4.3 Finding klmn:
//
// https://www.microsoft.com/en-us/research/wp-content/uploads/2005/01/p1000-loop.pdf
Sk2f T2 = t2/s2; // T2 is the double root of l(T).
Sk2f T1 = SkNx_shuffle<1,0>(T2); // T1 is the other root of l(T).
// Convert l(T), m(T) to power-basis form:
//
// | 1 1 |
// |l(T) m(T)| = |T^3 T^2 T 1| * | l2 m2 |
// | l1 m1 |
// | l0 m0 |
//
// From here on we use Sk2f with "L" names, but the second lane will be for line M.
Sk2f l2 = SkNx_fma(Sk2f(-2), T2, -T1);
Sk2f l1 = T2 * SkNx_fma(Sk2f(2), T1, T2);
Sk2f l0 = -T2*T2*T1;
// The equation for line L can be found as follows:
//
// L = C^-1 * (l excluding skipTerm)
//
// (See comments for GrPathUtils::calcCubicInverseTransposePowerBasisMatrix.)
// We are only interested in the normal to L, so only need the upper 2x2 of C^-1. And rather
// than divide by determinant(C) here, we have already performed this divide on padRadius.
Sk2f l2or1 = (ExcludedTerm::kLinearTerm == skipTerm) ? l2 : l1;
Sk2f Lx = -C0[1]*l2or1 + C1[1]; // l3 is always 1.
Sk2f Ly = C0[0]*l2or1 - C1[0];
// A box of radius "padRadius" is touching line L if "center dot L" is less than the Manhattan
// with of L. (See rationale in are_collinear.)
Sk2f Lwidth = Lx.abs() + Ly.abs();
Sk2f pad = Lwidth * padRadius;
// Is l(T=0) outside the padding around line L?
Sk2f lT0 = l0; // l(T=0) = |0 0 0 1| dot |1 l2 l1 l0| = l0
Sk2f outsideT0 = lT0.abs() - pad;
// Is l(T=1) outside the padding around line L?
Sk2f lT1 = (Sk2f(1) + l2 + l1 + l0).abs(); // l(T=1) = |1 1 1 1| dot |1 l2 l1 l0|
Sk2f outsideT1 = lT1.abs() - pad;
// Values for solving the cubic.
Sk2f p, q, qqq, discr, numRoots, D;
bool hasDiscr = false;
// Values for calculating one root (rarely needed).
Sk2f R, QQ;
bool hasOneRootVals = false;
// Values for calculating three roots.
Sk2f P, cosTheta3;
bool hasThreeRootVals = false;
// Solve for the T values where l(T) = +pad and m(T) = -pad.
for (int i = 0; i < 2; ++i) {
float T = T2[i]; // T is the point we are chopping around.
if ((T < 0 && outsideT0[i] >= 0) || (T > 1 && outsideT1[i] >= 0)) {
// The padding around T is completely out of range. No point solving for it.
continue;
}
if (!hasDiscr) {
p = Sk2f(+.5f, -.5f) * pad;
q = (1.f/3) * (T2 - T1);
qqq = q*q*q;
discr = qqq*p*2 + p*p;
numRoots = (discr < 0).thenElse(3, 1);
D = T2 - q;
hasDiscr = true;
}
if (1 == numRoots[i]) {
if (!hasOneRootVals) {
Sk2f r = qqq + p;
Sk2f s = r.abs() + discr.sqrt();
R = (r > 0).thenElse(-s, s);
QQ = q*q;
hasOneRootVals = true;
}
float A = cbrtf(R[i]);
float B = A != 0 ? QQ[i]/A : 0;
// When there is only one root, ine L chops from root..1, line M chops from 0..root.
if (1 == i) {
chops->push_back(0);
}
chops->push_back(A + B + D[i]);
if (0 == i) {
chops->push_back(1);
}
continue;
}
if (!hasThreeRootVals) {
P = q.abs() * -2;
cosTheta3 = (q >= 0).thenElse(1, -1) + p / qqq.abs();
hasThreeRootVals = true;
}
static constexpr float k2PiOver3 = 2 * SK_ScalarPI / 3;
float theta = std::acos(cosTheta3[i]) * (1.f/3);
float roots[3] = {P[i] * std::cos(theta) + D[i],
P[i] * std::cos(theta + k2PiOver3) + D[i],
P[i] * std::cos(theta - k2PiOver3) + D[i]};
// Sort the three roots.
swap_if_greater(roots[0], roots[1]);
swap_if_greater(roots[1], roots[2]);
swap_if_greater(roots[0], roots[1]);
// Line L chops around the first 2 roots, line M chops around the second 2.
chops->push_back_n(2, &roots[i]);
}
}
void GrCCFillGeometry::cubicTo(const SkPoint P[4], float inflectPad, float loopIntersectPad) {
SkASSERT(fBuildingContour);
SkASSERT(P[0] == fPoints.back());
// Don't crunch on the curve or inflate geometry if it is nearly flat (or just very small).
// Flat curves can break the math below.
if (are_collinear(P)) {
Sk2f p0 = Sk2f::Load(P);
Sk2f p3 = Sk2f::Load(P+3);
this->appendLine(p0, p3);
return;
}
Sk2f p0 = Sk2f::Load(P);
Sk2f p1 = Sk2f::Load(P+1);
Sk2f p2 = Sk2f::Load(P+2);
Sk2f p3 = Sk2f::Load(P+3);
// Also detect near-quadratics ahead of time.
Sk2f tan0, tan1, c;
get_cubic_tangents(p0, p1, p2, p3, &tan0, &tan1);
if (is_cubic_nearly_quadratic(p0, p1, p2, p3, tan0, tan1, &c)) {
this->appendQuadratics(p0, c, p3);
return;
}
double tt[2], ss[2], D[4];
fCurrCubicType = SkClassifyCubic(P, tt, ss, D);
SkASSERT(!SkCubicIsDegenerate(fCurrCubicType));
Sk2f t = Sk2f(static_cast<float>(tt[0]), static_cast<float>(tt[1]));
Sk2f s = Sk2f(static_cast<float>(ss[0]), static_cast<float>(ss[1]));
ExcludedTerm skipTerm = (std::abs(D[2]) > std::abs(D[1]))
? ExcludedTerm::kQuadraticTerm
: ExcludedTerm::kLinearTerm;
Sk2f C0 = SkNx_fma(Sk2f(3), p1 - p2, p3 - p0);
Sk2f C1 = (ExcludedTerm::kLinearTerm == skipTerm
? SkNx_fma(Sk2f(-2), p1, p0 + p2)
: p1 - p0) * 3;
Sk2f C0x1 = C0 * SkNx_shuffle<1,0>(C1);
float Cdet = C0x1[0] - C0x1[1];
SkSTArray<4, float> chops;
if (SkCubicType::kLoop != fCurrCubicType) {
find_chops_around_inflection_points(inflectPad, t, s, C0, C1, skipTerm, Cdet, &chops);
} else {
find_chops_around_loop_intersection(loopIntersectPad, t, s, C0, C1, skipTerm, Cdet, &chops);
}
if (4 == chops.count() && chops[1] >= chops[2]) {
// This just the means the KLM roots are so close that their paddings overlap. We will
// approximate the entire middle section, but still have it chopped midway. For loops this
// chop guarantees the append code only sees convex segments. Otherwise, it means we are (at
// least almost) a cusp and the chop makes sure we get a sharp point.
Sk2f ts = t * SkNx_shuffle<1,0>(s);
chops[1] = chops[2] = (ts[0] + ts[1]) / (2*s[0]*s[1]);
}
#ifdef SK_DEBUG
for (int i = 1; i < chops.count(); ++i) {
SkASSERT(chops[i] >= chops[i - 1]);
}
#endif
this->appendCubics(AppendCubicMode::kLiteral, p0, p1, p2, p3, chops.begin(), chops.count());
}
static inline void chop_cubic(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2, const Sk2f& p3,
float T, Sk2f* ab, Sk2f* abc, Sk2f* abcd, Sk2f* bcd, Sk2f* cd) {
Sk2f TT = T;
*ab = lerp(p0, p1, TT);
Sk2f bc = lerp(p1, p2, TT);
*cd = lerp(p2, p3, TT);
*abc = lerp(*ab, bc, TT);
*bcd = lerp(bc, *cd, TT);
*abcd = lerp(*abc, *bcd, TT);
}
void GrCCFillGeometry::appendCubics(AppendCubicMode mode, const Sk2f& p0, const Sk2f& p1,
const Sk2f& p2, const Sk2f& p3, const float chops[],
int numChops, float localT0, float localT1) {
if (numChops) {
SkASSERT(numChops > 0);
int midChopIdx = numChops/2;
float T = chops[midChopIdx];
// Chops alternate between literal and approximate mode.
AppendCubicMode rightMode = (AppendCubicMode)((bool)mode ^ (midChopIdx & 1) ^ 1);
if (T <= localT0) {
// T is outside 0..1. Append the right side only.
this->appendCubics(rightMode, p0, p1, p2, p3, &chops[midChopIdx + 1],
numChops - midChopIdx - 1, localT0, localT1);
return;
}
if (T >= localT1) {
// T is outside 0..1. Append the left side only.
this->appendCubics(mode, p0, p1, p2, p3, chops, midChopIdx, localT0, localT1);
return;
}
float localT = (T - localT0) / (localT1 - localT0);
Sk2f p01, p02, pT, p11, p12;
chop_cubic(p0, p1, p2, p3, localT, &p01, &p02, &pT, &p11, &p12);
this->appendCubics(mode, p0, p01, p02, pT, chops, midChopIdx, localT0, T);
this->appendCubics(rightMode, pT, p11, p12, p3, &chops[midChopIdx + 1],
numChops - midChopIdx - 1, T, localT1);
return;
}
this->appendCubics(mode, p0, p1, p2, p3);
}
void GrCCFillGeometry::appendCubics(AppendCubicMode mode, const Sk2f& p0, const Sk2f& p1,
const Sk2f& p2, const Sk2f& p3, int maxSubdivisions) {
if (SkCubicType::kLoop != fCurrCubicType) {
// Serpentines and cusps are always monotonic after chopping around inflection points.
SkASSERT(!SkCubicIsDegenerate(fCurrCubicType));
if (AppendCubicMode::kApproximate == mode) {
// This section passes through an inflection point, so we can get away with a flat line.
// This can cause some curves to feel slightly more flat when inspected rigorously back
// and forth against another renderer, but for now this seems acceptable given the
// simplicity.
this->appendLine(p0, p3);
return;
}
} else {
Sk2f tan0, tan1;
get_cubic_tangents(p0, p1, p2, p3, &tan0, &tan1);
if (maxSubdivisions && !is_convex_curve_monotonic(p0, tan0, p3, tan1)) {
this->chopAndAppendCubicAtMidTangent(mode, p0, p1, p2, p3, tan0, tan1,
maxSubdivisions - 1);
return;
}
if (AppendCubicMode::kApproximate == mode) {
Sk2f c;
if (!is_cubic_nearly_quadratic(p0, p1, p2, p3, tan0, tan1, &c) && maxSubdivisions) {
this->chopAndAppendCubicAtMidTangent(mode, p0, p1, p2, p3, tan0, tan1,
maxSubdivisions - 1);
return;
}
this->appendMonotonicQuadratic(p0, c, p3);
return;
}
}
// Don't send curves to the GPU if we know they are nearly flat (or just very small).
// Since the cubic segment is known to be convex at this point, our flatness check is simple.
if (are_collinear(p0, (p1 + p2) * .5f, p3)) {
this->appendLine(p0, p3);
return;
}
SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1]));
SkASSERT((p0 != p3).anyTrue());
p1.store(&fPoints.push_back());
p2.store(&fPoints.push_back());
p3.store(&fPoints.push_back());
fVerbs.push_back(Verb::kMonotonicCubicTo);
++fCurrContourTallies.fCubics;
}
// Given a convex curve segment with the following order-2 tangent function:
//
// |C2x C2y|
// tan = some_scale * |dx/dt dy/dt| = |t^2 t 1| * |C1x C1y|
// |C0x C0y|
//
// This function finds the T value whose tangent angle is halfway between the tangents at T=0 and
// T=1 (tan0 and tan1).
static inline float find_midtangent(const Sk2f& tan0, const Sk2f& tan1,
const Sk2f& C2, const Sk2f& C1, const Sk2f& C0) {
// Tangents point in the direction of increasing T, so tan0 and -tan1 both point toward the
// midtangent. 'n' will therefore bisect tan0 and -tan1, giving us the normal to the midtangent.
//
// n dot midtangent = 0
//
Sk2f n = normalize(tan0) - normalize(tan1);
// Find the T value at the midtangent. This is a simple quadratic equation:
//
// midtangent dot n = 0
//
// (|t^2 t 1| * C) dot n = 0
//
// |t^2 t 1| dot C*n = 0
//
// First find coeffs = C*n.
Sk4f C[2];
Sk2f::Store4(C, C2, C1, C0, 0);
Sk4f coeffs = C[0]*n[0] + C[1]*n[1];
// Now solve the quadratic.
float a = coeffs[0], b = coeffs[1], c = coeffs[2];
float discr = b*b - 4*a*c;
if (discr < 0) {
return 0; // This will only happen if the curve is a line.
}
// The roots are q/a and c/q. Pick the one closer to T=.5.
float q = -.5f * (b + copysignf(std::sqrt(discr), b));
float r = .5f*q*a;
return std::abs(q*q - r) < std::abs(a*c - r) ? q/a : c/q;
}
inline void GrCCFillGeometry::chopAndAppendCubicAtMidTangent(AppendCubicMode mode, const Sk2f& p0,
const Sk2f& p1, const Sk2f& p2,
const Sk2f& p3, const Sk2f& tan0,
const Sk2f& tan1,
int maxFutureSubdivisions) {
float midT = find_midtangent(tan0, tan1, p3 + (p1 - p2)*3 - p0,
(p0 - p1*2 + p2)*2,
p1 - p0);
// Use positive logic since NaN fails comparisons. (However midT should not be NaN since we cull
// near-flat cubics in cubicTo().)
if (!(midT > 0 && midT < 1)) {
// The cubic is flat. Otherwise there would be a real midtangent inside T=0..1.
this->appendLine(p0, p3);
return;
}
Sk2f p01, p02, pT, p11, p12;
chop_cubic(p0, p1, p2, p3, midT, &p01, &p02, &pT, &p11, &p12);
this->appendCubics(mode, p0, p01, p02, pT, maxFutureSubdivisions);
this->appendCubics(mode, pT, p11, p12, p3, maxFutureSubdivisions);
}
void GrCCFillGeometry::conicTo(const SkPoint P[3], float w) {
SkASSERT(fBuildingContour);
SkASSERT(P[0] == fPoints.back());
Sk2f p0 = Sk2f::Load(P);
Sk2f p1 = Sk2f::Load(P+1);
Sk2f p2 = Sk2f::Load(P+2);
Sk2f tan0 = p1 - p0;
Sk2f tan1 = p2 - p1;
if (!is_convex_curve_monotonic(p0, tan0, p2, tan1)) {
// The derivative of a conic has a cumbersome order-4 denominator. However, this isn't
// necessary if we are only interested in a vector in the same *direction* as a given
// tangent line. Since the denominator scales dx and dy uniformly, we can throw it out
// completely after evaluating the derivative with the standard quotient rule. This leaves
// us with a simpler quadratic function that we use to find the midtangent.
float midT = find_midtangent(tan0, tan1, (w - 1) * (p2 - p0),
(p2 - p0) - 2*w*(p1 - p0),
w*(p1 - p0));
// Use positive logic since NaN fails comparisons. (However midT should not be NaN since we
// cull near-linear conics above. And while w=0 is flat, it's not a line and has valid
// midtangents.)
if (!(midT > 0 && midT < 1)) {
// The conic is flat. Otherwise there would be a real midtangent inside T=0..1.
this->appendLine(p0, p2);
return;
}
// Chop the conic at midtangent to produce two monotonic segments.
Sk4f p3d0 = Sk4f(p0[0], p0[1], 1, 0);
Sk4f p3d1 = Sk4f(p1[0], p1[1], 1, 0) * w;
Sk4f p3d2 = Sk4f(p2[0], p2[1], 1, 0);
Sk4f midT4 = midT;
Sk4f p3d01 = lerp(p3d0, p3d1, midT4);
Sk4f p3d12 = lerp(p3d1, p3d2, midT4);
Sk4f p3d012 = lerp(p3d01, p3d12, midT4);
Sk2f midpoint = Sk2f(p3d012[0], p3d012[1]) / p3d012[2];
Sk2f ww = Sk2f(p3d01[2], p3d12[2]) * Sk2f(p3d012[2]).rsqrt();
this->appendMonotonicConic(p0, Sk2f(p3d01[0], p3d01[1]) / p3d01[2], midpoint, ww[0]);
this->appendMonotonicConic(midpoint, Sk2f(p3d12[0], p3d12[1]) / p3d12[2], p2, ww[1]);
return;
}
this->appendMonotonicConic(p0, p1, p2, w);
}
void GrCCFillGeometry::appendMonotonicConic(const Sk2f& p0, const Sk2f& p1, const Sk2f& p2,
float w) {
SkASSERT(w >= 0);
Sk2f base = p2 - p0;
Sk2f baseAbs = base.abs();
float baseWidth = baseAbs[0] + baseAbs[1];
// Find the height of the curve. Max height always occurs at T=.5 for conics.
Sk2f d = (p1 - p0) * SkNx_shuffle<1,0>(base);
float h1 = std::abs(d[1] - d[0]); // Height of p1 above the base.
float ht = h1*w, hs = 1 + w; // Height of the conic = ht/hs.
// i.e. (ht/hs <= baseWidth * kFlatnessThreshold). Use "<=" in case base == 0.
if (ht <= (baseWidth*hs) * kFlatnessThreshold) {
// We are flat. (See rationale in are_collinear.)
this->appendLine(p0, p2);
return;
}
// i.e. (w > 1 && h1 - ht/hs < baseWidth).
if (w > 1 && h1*hs - ht < baseWidth*hs) {
// If we get within 1px of p1 when w > 1, we will pick up artifacts from the implicit
// function's reflection. Chop at max height (T=.5) and draw a triangle instead.
Sk2f p1w = p1*w;
Sk2f ab = p0 + p1w;
Sk2f bc = p1w + p2;
Sk2f highpoint = (ab + bc) / (2*(1 + w));
this->appendLine(p0, highpoint);
this->appendLine(highpoint, p2);
return;
}
SkASSERT(fPoints.back() == SkPoint::Make(p0[0], p0[1]));
SkASSERT((p0 != p2).anyTrue());
p1.store(&fPoints.push_back());
p2.store(&fPoints.push_back());
fConicWeights.push_back(w);
fVerbs.push_back(Verb::kMonotonicConicTo);
++fCurrContourTallies.fConics;
}
GrCCFillGeometry::PrimitiveTallies GrCCFillGeometry::endContour() {
SkASSERT(fBuildingContour);
SkASSERT(fVerbs.count() >= fCurrContourTallies.fTriangles);
// The fTriangles field currently contains this contour's starting verb index. We can now
// use it to calculate the size of the contour's fan.
int fanSize = fVerbs.count() - fCurrContourTallies.fTriangles;
if (fPoints.back() == fCurrAnchorPoint) {
--fanSize;
fVerbs.push_back(Verb::kEndClosedContour);
} else {
fVerbs.push_back(Verb::kEndOpenContour);
}
fCurrContourTallies.fTriangles = SkTMax(fanSize - 2, 0);
SkDEBUGCODE(fBuildingContour = false);
return fCurrContourTallies;
}