/*
* Copyright 2006 The Android Open Source Project
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "src/core/SkAnalyticEdge.h"
#include "include/core/SkPoint.h"
#include "include/private/base/SkMath.h"
#include "include/private/base/SkTo.h"
#include "src/core/SkFDot6.h"
#include <algorithm>
#include <cstddef>
#include <iterator>
static const int kInverseTableSize = 1024;
// SK_FDot6One * 16
static inline SkFixed quick_inverse(SkFDot6 x) {
static const int32_t table[] = {
-4096, -4100, -4104, -4108, -4112, -4116, -4120, -4124, -4128, -4132, -4136,
-4140, -4144, -4148, -4152, -4156, -4161, -4165, -4169, -4173, -4177, -4181,
-4185, -4190, -4194, -4198, -4202, -4206, -4211, -4215, -4219, -4223, -4228,
-4232, -4236, -4240, -4245, -4249, -4253, -4258, -4262, -4266, -4271, -4275,
-4279, -4284, -4288, -4293, -4297, -4301, -4306, -4310, -4315, -4319, -4324,
-4328, -4332, -4337, -4341, -4346, -4350, -4355, -4359, -4364, -4369, -4373,
-4378, -4382, -4387, -4391, -4396, -4401, -4405, -4410, -4415, -4419, -4424,
-4429, -4433, -4438, -4443, -4447, -4452, -4457, -4462, -4466, -4471, -4476,
-4481, -4485, -4490, -4495, -4500, -4505, -4510, -4514, -4519, -4524, -4529,
-4534, -4539, -4544, -4549, -4554, -4559, -4563, -4568, -4573, -4578, -4583,
-4588, -4593, -4599, -4604, -4609, -4614, -4619, -4624, -4629, -4634, -4639,
-4644, -4650, -4655, -4660, -4665, -4670, -4675, -4681, -4686, -4691, -4696,
-4702, -4707, -4712, -4718, -4723, -4728, -4733, -4739, -4744, -4750, -4755,
-4760, -4766, -4771, -4777, -4782, -4788, -4793, -4798, -4804, -4809, -4815,
-4821, -4826, -4832, -4837, -4843, -4848, -4854, -4860, -4865, -4871, -4877,
-4882, -4888, -4894, -4899, -4905, -4911, -4917, -4922, -4928, -4934, -4940,
-4946, -4951, -4957, -4963, -4969, -4975, -4981, -4987, -4993, -4999, -5005,
-5011, -5017, -5023, -5029, -5035, -5041, -5047, -5053, -5059, -5065, -5071,
-5077, -5084, -5090, -5096, -5102, -5108, -5115, -5121, -5127, -5133, -5140,
-5146, -5152, -5159, -5165, -5171, -5178, -5184, -5190, -5197, -5203, -5210,
-5216, -5223, -5229, -5236, -5242, -5249, -5256, -5262, -5269, -5275, -5282,
-5289, -5295, -5302, -5309, -5315, -5322, -5329, -5336, -5343, -5349, -5356,
-5363, -5370, -5377, -5384, -5391, -5398, -5405, -5412, -5418, -5426, -5433,
-5440, -5447, -5454, -5461, -5468, -5475, -5482, -5489, -5497, -5504, -5511,
-5518, -5526, -5533, -5540, -5548, -5555, -5562, -5570, -5577, -5584, -5592,
-5599, -5607, -5614, -5622, -5629, -5637, -5645, -5652, -5660, -5667, -5675,
-5683, -5691, -5698, -5706, -5714, -5722, -5729, -5737, -5745, -5753, -5761,
-5769, -5777, -5785, -5793, -5801, -5809, -5817, -5825, -5833, -5841, -5849,
-5857, -5866, -5874, -5882, -5890, -5899, -5907, -5915, -5924, -5932, -5940,
-5949, -5957, -5966, -5974, -5983, -5991, -6000, -6009, -6017, -6026, -6034,
-6043, -6052, -6061, -6069, -6078, -6087, -6096, -6105, -6114, -6123, -6132,
-6141, -6150, -6159, -6168, -6177, -6186, -6195, -6204, -6213, -6223, -6232,
-6241, -6250, -6260, -6269, -6278, -6288, -6297, -6307, -6316, -6326, -6335,
-6345, -6355, -6364, -6374, -6384, -6393, -6403, -6413, -6423, -6432, -6442,
-6452, -6462, -6472, -6482, -6492, -6502, -6512, -6523, -6533, -6543, -6553,
-6563, -6574, -6584, -6594, -6605, -6615, -6626, -6636, -6647, -6657, -6668,
-6678, -6689, -6700, -6710, -6721, -6732, -6743, -6754, -6765, -6775, -6786,
-6797, -6808, -6820, -6831, -6842, -6853, -6864, -6875, -6887, -6898, -6909,
-6921, -6932, -6944, -6955, -6967, -6978, -6990, -7002, -7013, -7025, -7037,
-7049, -7061, -7073, -7084, -7096, -7108, -7121, -7133, -7145, -7157, -7169,
-7182, -7194, -7206, -7219, -7231, -7244, -7256, -7269, -7281, -7294, -7307,
-7319, -7332, -7345, -7358, -7371, -7384, -7397, -7410, -7423, -7436, -7449,
-7463, -7476, -7489, -7503, -7516, -7530, -7543, -7557, -7570, -7584, -7598,
-7612, -7626, -7639, -7653, -7667, -7681, -7695, -7710, -7724, -7738, -7752,
-7767, -7781, -7796, -7810, -7825, -7839, -7854, -7869, -7884, -7898, -7913,
-7928, -7943, -7958, -7973, -7989, -8004, -8019, -8035, -8050, -8065, -8081,
-8097, -8112, -8128, -8144, -8160, -8176, -8192, -8208, -8224, -8240, -8256,
-8272, -8289, -8305, -8322, -8338, -8355, -8371, -8388, -8405, -8422, -8439,
-8456, -8473, -8490, -8507, -8525, -8542, -8559, -8577, -8594, -8612, -8630,
-8648, -8665, -8683, -8701, -8719, -8738, -8756, -8774, -8793, -8811, -8830,
-8848, -8867, -8886, -8905, -8924, -8943, -8962, -8981, -9000, -9020, -9039,
-9058, -9078, -9098, -9118, -9137, -9157, -9177, -9198, -9218, -9238, -9258,
-9279, -9300, -9320, -9341, -9362, -9383, -9404, -9425, -9446, -9467, -9489,
-9510, -9532, -9554, -9576, -9597, -9619, -9642, -9664, -9686, -9709, -9731,
-9754, -9776, -9799, -9822, -9845, -9868, -9892, -9915, -9939, -9962, -9986,
-10010, -10034, -10058, -10082, -10106, -10131, -10155, -10180, -10205, -10230,
-10255, -10280, -10305, -10330, -10356, -10381, -10407, -10433, -10459, -10485,
-10512, -10538, -10564, -10591, -10618, -10645, -10672, -10699, -10727, -10754,
-10782, -10810, -10837, -10866, -10894, -10922, -10951, -10979, -11008, -11037,
-11066, -11096, -11125, -11155, -11184, -11214, -11244, -11275, -11305, -11335,
-11366, -11397, -11428, -11459, -11491, -11522, -11554, -11586, -11618, -11650,
-11683, -11715, -11748, -11781, -11814, -11848, -11881, -11915, -11949, -11983,
-12018, -12052, -12087, -12122, -12157, -12192, -12228, -12264, -12300, -12336,
-12372, -12409, -12446, -12483, -12520, -12557, -12595, -12633, -12671, -12710,
-12748, -12787, -12826, -12865, -12905, -12945, -12985, -13025, -13066, -13107,
-13148, -13189, -13231, -13273, -13315, -13357, -13400, -13443, -13486, -13530,
-13573, -13617, -13662, -13706, -13751, -13797, -13842, -13888, -13934, -13981,
-14027, -14074, -14122, -14169, -14217, -14266, -14315, -14364, -14413, -14463,
-14513, -14563, -14614, -14665, -14716, -14768, -14820, -14873, -14926, -14979,
-15033, -15087, -15141, -15196, -15252, -15307, -15363, -15420, -15477, -15534,
-15592, -15650, -15709, -15768, -15827, -15887, -15947, -16008, -16070, -16131,
-16194, -16256, -16320, -16384, -16448, -16513, -16578, -16644, -16710, -16777,
-16844, -16912, -16980, -17050, -17119, -17189, -17260, -17331, -17403, -17476,
-17549, -17623, -17697, -17772, -17848, -17924, -18001, -18078, -18157, -18236,
-18315, -18396, -18477, -18558, -18641, -18724, -18808, -18893, -18978, -19065,
-19152, -19239, -19328, -19418, -19508, -19599, -19691, -19784, -19878, -19972,
-20068, -20164, -20262, -20360, -20460, -20560, -20661, -20763, -20867, -20971,
-21076, -21183, -21290, -21399, -21509, -21620, -21732, -21845, -21959, -22075,
-22192, -22310, -22429, -22550, -22671, -22795, -22919, -23045, -23172, -23301,
-23431, -23563, -23696, -23831, -23967, -24105, -24244, -24385, -24528, -24672,
-24818, -24966, -25115, -25266, -25420, -25575, -25731, -25890, -26051, -26214,
-26379, -26546, -26715, -26886, -27060, -27235, -27413, -27594, -27776, -27962,
-28149, -28339, -28532, -28728, -28926, -29127, -29330, -29537, -29746, -29959,
-30174, -30393, -30615, -30840, -31068, -31300, -31536, -31775, -32017, -32263,
-32513, -32768, -33026, -33288, -33554, -33825, -34100, -34379, -34663, -34952,
-35246, -35544, -35848, -36157, -36472, -36792, -37117, -37449, -37786, -38130,
-38479, -38836, -39199, -39568, -39945, -40329, -40721, -41120, -41527, -41943,
-42366, -42799, -43240, -43690, -44150, -44620, -45100, -45590, -46091, -46603,
-47127, -47662, -48210, -48770, -49344, -49932, -50533, -51150, -51781, -52428,
-53092, -53773, -54471, -55188, -55924, -56679, -57456, -58254, -59074, -59918,
-60787, -61680, -62601, -63550, -64527, -65536, -66576, -67650, -68759, -69905,
-71089, -72315, -73584, -74898, -76260, -77672, -79137, -80659, -82241, -83886,
-85598, -87381, -89240, -91180, -93206, -95325, -97541, -99864, -102300,
-104857, -107546, -110376, -113359, -116508, -119837, -123361, -127100, -131072,
-135300, -139810, -144631, -149796, -155344, -161319, -167772, -174762, -182361,
-190650, -199728, -209715, -220752, -233016, -246723, -262144, -279620, -299593,
-322638, -349525, -381300, -419430, -466033, -524288, -599186, -699050, -838860,
-1048576, -1398101, -2097152, -4194304, 0
};
static constexpr size_t kLastEntry = std::size(table) - 1;
SkASSERT(SkAbs32(x) <=
static_cast<int32_t>(kLastEntry));
static_assert(kLastEntry == kInverseTableSize);
if (x > 0) {
return -table[kLastEntry - x];
}
else {
return table[kLastEntry + x];
}
}
static inline SkFixed quick_div(SkFDot6 a, SkFDot6 b) {
const int kMinBits = 3;
// abs(b) should be at least (1 << kMinBits) for quick division
const int kMaxBits = 31;
// Number of bits available in signed int
// Given abs(b) <= (1 << kMinBits), the inverse of abs(b) is at most 1 << (22 - kMinBits) in
// SkFixed format. Hence abs(a) should be less than kMaxAbsA
const int kMaxAbsA = 1 << (kMaxBits - (22 - kMinBits));
SkFDot6 abs_a = SkAbs32(a);
SkFDot6 abs_b = SkAbs32(b);
if (abs_b >= (1 << kMinBits) && abs_b < kInverseTableSize && abs_a < kMaxAbsA) {
SkASSERT((int64_t)a * quick_inverse(b) <= SK_MaxS32
&& (int64_t)a * quick_inverse(b) >= SK_MinS32);
SkFixed ourAnswer = (a * quick_inverse(b)) >> 6;
SkASSERT(
(SkFDot6Div(a,b) == 0 && ourAnswer == 0) ||
SkFixedDiv(SkAbs32(SkFDot6Div(a,b) - ourAnswer), SkAbs32(SkFDot6Div(a,b))) <= 1 << 10
);
return ourAnswer;
}
return SkFDot6Div(a, b);
}
bool SkAnalyticEdge::setLine(
const SkPoint& p0,
const SkPoint& p1) {
// We must set X/Y using the same way (e.g., times 4, to FDot6, then to Fixed) as Quads/Cubics.
// Otherwise the order of the edge might be wrong due to precision limit.
const int accuracy = kDefaultAccuracy;
#ifdef SK_RASTERIZE_EVEN_ROUNDING
SkFixed x0 = SkFDot6ToFixed(SkScalarRoundToFDot6(p0.fX, accuracy)) >> accuracy;
SkFixed y0 = SnapY(SkFDot6ToFixed(SkScalarRoundToFDot6(p0.fY, accuracy)) >> accuracy);
SkFixed x1 = SkFDot6ToFixed(SkScalarRoundToFDot6(p1.fX, accuracy)) >> accuracy;
SkFixed y1 = SnapY(SkFDot6ToFixed(SkScalarRoundToFDot6(p1.fY, accuracy)) >> accuracy);
#else
const int multiplier = (1 << kDefaultAccuracy);
SkFixed x0 = SkFDot6ToFixed(SkScalarToFDot6(p0.fX * multiplier)) >> accuracy;
SkFixed y0 = SnapY(SkFDot6ToFixed(SkScalarToFDot6(p0.fY * multiplier)) >> accuracy);
SkFixed x1 = SkFDot6ToFixed(SkScalarToFDot6(p1.fX * multiplier)) >> accuracy;
SkFixed y1 = SnapY(SkFDot6ToFixed(SkScalarToFDot6(p1.fY * multiplier)) >> accuracy);
#endif
int winding = 1;
if (y0 > y1) {
using std::swap;
swap(x0, x1);
swap(y0, y1);
winding = -1;
}
// are we a zero-height line?
SkFDot6 dy = SkFixedToFDot6(y1 - y0);
if (dy == 0) {
return false;
}
SkFDot6 dx = SkFixedToFDot6(x1 - x0);
SkFixed slope = quick_div(dx, dy);
SkFixed absSlope = SkAbs32(slope);
fX = x0;
fDX = slope;
fUpperX = x0;
fY = y0;
fUpperY = y0;
fLowerY = y1;
fDY = dx == 0 || slope == 0 ? SK_MaxS32 : absSlope < kInverseTableSize
? quick_inverse(absSlope)
: SkAbs32(quick_div(dy, dx));
fEdgeType = kLine_Type;
fCurveCount = 0;
fWinding = SkToS8(winding);
fCurveShift = 0;
return true;
}
// This will become a bottleneck for small ovals rendering if we call SkFixedDiv twice here.
// Therefore, we'll let the outter function compute the slope once and send in the value.
// Moreover, we'll compute fDY by quickly lookup the inverse table (if possible).
bool SkAnalyticEdge::updateLine(SkFixed x0, SkFixed y0, SkFixed x1, SkFixed y1, SkFixed sl
ope) {
// Since we send in the slope, we can no longer snap y inside this function.
// If we don't send in the slope, or we do some more sophisticated snapping, this function
// could be a performance bottleneck.
SkASSERT(fWinding == 1 || fWinding == -1);
SkASSERT(fCurveCount != 0);
// We don't chop at y extrema for cubics so the y is not guaranteed to be increasing for them.
// In that case, we have to swap x/y and negate the winding.
if (y0 > y1) {
using std::swap;
swap(x0, x1);
swap(y0, y1);
fWinding = -fWinding;
}
SkASSERT(y0 <= y1);
SkFDot6 dx = SkFixedToFDot6(x1 - x0);
SkFDot6 dy = SkFixedToFDot6(y1 - y0);
// are we a zero-height line?
if (dy == 0) {
return false;
}
SkASSERT(slope < SK_MaxS32);
SkFDot6 absSlope = SkAbs32(SkFixedToFDot6(slope));
fX = x0;
fDX = slope;
fUpperX = x0;
fY = y0;
fUpperY = y0;
fLowerY = y1;
fDY = (dx == 0 || slope == 0)
? SK_MaxS32
: absSlope < kInverseTableSize
? quick_inverse(absSlope)
: SkAbs32(quick_div(dy, dx));
return true;
}
bool SkAnalyticEdge::update(SkFixed last_y, bool sortY) {
SkASSERT(last_y >= fLowerY); // we shouldn't update edge if last_y < fLowerY
if (fCurveCount < 0) {
return static_cast<SkAnalyticCubicEdge*>(this)->updateCubic(sortY);
} else if (fCurveCount > 0) {
return static_cast<SkAnalyticQuadraticEdge*>(this)->updateQuadratic();
}
return false;
}
bool SkAnalyticQuadraticEdge::setQuadratic(const SkPoint pts[3]) {
if (!fQEdge.setQuadraticWithoutUpdate(pts, kDefaultAccuracy)) {
return false;
}
fQEdge.fQx >>= kDefaultAccuracy;
fQEdge.fQy >>= kDefaultAccuracy;
fQEdge.fQDx >>= kDefaultAccuracy;
fQEdge.fQDy >>= kDefaultAccuracy;
fQEdge.fQDDx >>= kDefaultAccuracy;
fQEdge.fQDDy >>= kDefaultAccuracy;
fQEdge.fQLastX >>= kDefaultAccuracy;
fQEdge.fQLastY >>= kDefaultAccuracy;
fQEdge.fQy = SnapY(fQEdge.fQy);
fQEdge.fQLastY = SnapY(fQEdge.fQLastY);
fWinding = fQEdge.fWinding;
fEdgeType = kQuad_Type;
fCurveCount = fQEdge.fCurveCount;
fCurveShift = fQEdge.fCurveShift;
fSnappedX = fQEdge.fQx;
fSnappedY = fQEdge.fQy;
return this->updateQuadratic();
}
bool SkAnalyticQuadraticEdge::updateQuadratic() {
int success = 0; // initialize to fail!
int count = fCurveCount;
SkFixed oldx = fQEdge.fQx;
SkFixed oldy = fQEdge.fQy;
SkFixed dx = fQEdge.fQDx;
SkFixed dy = fQEdge.fQDy;
SkFixed newx, newy, newSnappedX, newSnappedY;
int shift = fCurveShift;
SkASSERT(count > 0);
do {
SkFixed slope;
if (--count > 0)
{
newx = oldx + (dx >> shift);
newy = oldy + (dy >> shift);
if (SkAbs32(dy >> shift) >= SK_Fixed1 * 2) { // only snap when dy is large enough
SkFDot6 diffY = SkFixedToFDot6(newy - fSnappedY);
slope = diffY ? quick_div(SkFixedToFDot6(newx - fSnappedX), diffY)
: SK_MaxS32;
newSnappedY = std::min<SkFixed>(fQEdge.fQLastY, SkFixedRoundToFixed(newy));
newSnappedX = newx - SkFixedMul(slope, newy - newSnappedY);
} else {
newSnappedY = std::min(fQEdge.fQLastY, SnapY(newy));
newSnappedX = newx;
SkFDot6 diffY = SkFixedToFDot6(newSnappedY - fSnappedY);
slope = diffY ? quick_div(SkFixedToFDot6(newx - fSnappedX), diffY)
: SK_MaxS32;
}
dx += fQEdge.fQDDx;
dy += fQEdge.fQDDy;
}
else // last segment
{
newx = fQEdge.fQLastX;
newy = fQEdge.fQLastY;
newSnappedY = newy;
newSnappedX = newx;
SkFDot6 diffY = (newy - fSnappedY) >> 10;
slope = diffY ? quick_div((newx - fSnappedX) >> 10, diffY) : SK_MaxS32;
}
if (slope < SK_MaxS32) {
success = this->updateLine(fSnappedX, fSnappedY, newSnappedX, newSnappedY, slope);
}
oldx = newx;
oldy = newy;
} while (count > 0 && !success);
SkASSERT(newSnappedY <= fQEdge.fQLastY);
fQEdge.fQx = newx;
fQEdge.fQy = newy;
fQEdge.fQDx = dx;
fQEdge.fQDy = dy;
fSnappedX = newSnappedX;
fSnappedY = newSnappedY;
fCurveCount = SkToS8(count);
return success;
}
bool SkAnalyticCubicEdge::setCubic(const SkPoint pts[4], bool sortY) {
if (!fCEdge.setCubicWithoutUpdate(pts, kDefaultAccuracy, sortY)) {
return false;
}
fCEdge.fCx >>= kDefaultAccuracy;
fCEdge.fCy >>= kDefaultAccuracy;
fCEdge.fCDx >>= kDefaultAccuracy;
fCEdge.fCDy >>= kDefaultAccuracy;
fCEdge.fCDDx >>= kDefaultAccuracy;
fCEdge.fCDDy >>= kDefaultAccuracy;
fCEdge.fCDDDx >>= kDefaultAccuracy;
fCEdge.fCDDDy >>= kDefaultAccuracy;
fCEdge.fCLastX >>= kDefaultAccuracy;
fCEdge.fCLastY >>= kDefaultAccuracy;
fCEdge.fCy = SnapY(fCEdge.fCy);
fCEdge.fCLastY = SnapY(fCEdge.fCLastY);
fWinding = fCEdge.fWinding;
fEdgeType = kCubic_Type;
fCurveCount = fCEdge.fCurveCount;
fCurveShift = fCEdge.fCurveShift;
fCubicDShift = fCEdge.fCubicDShift;
fSnappedY = fCEdge.fCy;
return this->updateCubic(sortY);
}
bool SkAnalyticCubicEdge::updateCubic(bool sortY) {
int success;
int count = fCurveCount;
SkFixed oldx = fCEdge.fCx;
SkFixed oldy = fCEdge.fCy;
SkFixed newx, newy;
const int ddshift = fCurveShift;
const int dshift = fCubicDShift;
SkASSERT(count < 0);
do {
if (++count < 0) {
newx = oldx + (fCEdge.fCDx >> dshift);
fCEdge.fCDx += fCEdge.fCDDx >> ddshift;
fCEdge.fCDDx += fCEdge.fCDDDx;
newy = oldy + (fCEdge.fCDy >> dshift);
fCEdge.fCDy += fCEdge.fCDDy >> ddshift;
fCEdge.fCDDy += fCEdge.fCDDDy;
}
else { // last segment
newx = fCEdge.fCLastX;
newy = fCEdge.fCLastY;
}
// we want to say SkASSERT(oldy <= newy), but our finite fixedpoint
// doesn't always achieve that, so we have to explicitly pin it here.
if (sortY && newy < oldy) {
newy = oldy;
}
SkFixed newSnappedY = SnapY(newy);
// we want to SkASSERT(snappedNewY <= fCEdge.fCLastY), but our finite fixedpoint
// doesn't always achieve that, so we have to explicitly pin it here.
if (sortY && fCEdge.fCLastY < newSnappedY) {
newSnappedY = fCEdge.fCLastY;
count = 0;
}
SkFixed slope = SkFixedToFDot6(newSnappedY - fSnappedY) == 0
? SK_MaxS32
: SkFDot6Div(SkFixedToFDot6(newx - oldx),
SkFixedToFDot6(newSnappedY - fSnappedY));
success = this->updateLine(oldx, fSnappedY, newx, newSnappedY, slope);
oldx = newx;
oldy = newy;
fSnappedY = newSnappedY;
} while (count < 0 && !success);
fCEdge.fCx = newx;
fCEdge.fCy = newy;
fCurveCount = SkToS8(count);
return success;
}
