/*
* Copyright 2012 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "src/pathops/SkReduceOrder.h"
#include "include/core/SkPoint.h"
#include "src/core/SkGeometry.h"
#include "src/pathops/SkPathOpsPoint.h"
#include "src/pathops/SkPathOpsTypes.h"
#include <algorithm>
#include <cmath>
int SkReduceOrder::reduce(
const SkDLine& line) {
fLine[0] = line[0];
int different = line[0] != line[1];
fLine[1] = line[different];
return 1 + different;
}
static int coincident_line(
const SkDQuad& quad, SkDQuad& reduction) {
reduction[0] = reduction[1] = quad[0];
return 1;
}
static int reductionLineCount(
const SkDQuad& reduction) {
return 1 + !reduction[0].approximatelyEqual(reduction[1]);
}
static int vertical_line(
const SkDQuad& quad, SkDQuad& reduction) {
reduction[0] = quad[0];
reduction[1] = quad[2];
return reductionLineCount(reduction);
}
static int horizontal_line(
const SkDQuad& quad, SkDQuad& reduction) {
reduction[0] = quad[0];
reduction[1] = quad[2];
return reductionLineCount(reduction);
}
static int check_linear(
const SkDQuad& quad,
int minX,
int maxX,
int minY,
int maxY, SkDQuad& reduction) {
if (!quad.isLinear(0, 2)) {
return 0;
}
// four are colinear: return line formed by outside
reduction[0] = quad[0];
reduction[1] = quad[2];
return reductionLineCount(reduction);
}
// reduce to a quadratic or smaller
// look for identical points
// look for all four points in a line
// note that three points in a line doesn't simplify a cubic
// look for approximation with single quadratic
// save approximation with multiple quadratics for later
int SkReduceOrder::reduce(
const SkDQuad& quad) {
int index, minX, maxX, minY, maxY;
int minXSet, minYSet;
minX = maxX = minY = maxY = 0;
minXSet = minYSet = 0;
for (index = 1; index < 3; ++index) {
if (quad[minX].fX > quad[index].fX) {
minX = index;
}
if (quad[minY].fY > quad[index].fY) {
minY = index;
}
if (quad[maxX].fX < quad[index].fX) {
maxX = index;
}
if (quad[maxY].fY < quad[index].fY) {
maxY = index;
}
}
for (index = 0; index < 3; ++index) {
if (AlmostEqualUlps(quad[index].fX, quad[minX].fX)) {
minXSet |= 1 << index;
}
if (AlmostEqualUlps(quad[index].fY, quad[minY].fY)) {
minYSet |= 1 << index;
}
}
if ((minXSet & 0x05) == 0x5 && (minYSet & 0x05) == 0x5) {
// test for degenerate
// this quad starts and ends at the same place, so never contributes
// to the fill
return coincident_line(quad, fQuad);
}
if (minXSet == 0x7) {
// test for vertical line
return vertical_line(quad, fQuad);
}
if (minYSet == 0x7) {
// test for horizontal line
return horizontal_line(quad, fQuad);
}
int result = check_linear(quad, minX, maxX, minY, maxY, fQuad);
if (result) {
return result;
}
fQuad = quad;
return 3;
}
////////////////////////////////////////////////////////////////////////////////////
static int coincident_line(
const SkDCubic& cubic, SkDCubic& reduction) {
reduction[0] = reduction[1] = cubic[0];
return 1;
}
static int reductionLineCount(
const SkDCubic& reduction) {
return 1 + !reduction[0].approximatelyEqual(reduction[1]);
}
static int vertical_line(
const SkDCubic& cubic, SkDCubic& reduction) {
reduction[0] = cubic[0];
reduction[1] = cubic[3];
return reductionLineCount(reduction);
}
static int horizontal_line(
const SkDCubic& cubic, SkDCubic& reduction) {
reduction[0] = cubic[0];
reduction[1] = cubic[3];
return reductionLineCount(reduction);
}
// check to see if it is a quadratic or a line
static int check_quadratic(
const SkDCubic& cubic, SkDCubic& reduction) {
double dx10 = cubic[1].fX - cubic[0].fX;
double dx23 = cubic[2].fX - cubic[3].fX;
double midX = cubic[0].fX + dx10 * 3 / 2;
double sideAx = midX - cubic[3].fX;
double sideBx = dx23 * 3 / 2;
if (approximately_zero(sideAx) ? !approximately_equal(sideAx, sideBx)
: !AlmostEqualUlps_Pin(sideAx, sideBx)) {
return 0;
}
double dy10 = cubic[1].fY - cubic[0].fY;
double dy23 = cubic[2].fY - cubic[3].fY;
double midY = cubic[0].fY + dy10 * 3 / 2;
double sideAy = midY - cubic[3].fY;
double sideBy = dy23 * 3 / 2;
if (approximately_zero(sideAy) ? !approximately_equal(sideAy, sideBy)
: !AlmostEqualUlps_Pin(sideAy, sideBy)) {
return 0;
}
reduction[0] = cubic[0];
reduction[1].fX = midX;
reduction[1].fY = midY;
reduction[2] = cubic[3];
return 3;
}
static int check_linear(
const SkDCubic& cubic,
int minX,
int maxX,
int minY,
int maxY, SkDCubic& reduction) {
if (!cubic.isLinear(0, 3)) {
return 0;
}
// four are colinear: return line formed by outside
reduction[0] = cubic[0];
reduction[1] = cubic[3];
return reductionLineCount(reduction);
}
/* food for thought:
http://objectmix.com/graphics/132906-fast-precision-driven-cubic-quadratic-piecewise-degree-reduction-algos-2-a.html
Given points c1, c2, c3 and c4 of a cubic Bezier, the points of the
corresponding quadratic Bezier are (given in convex combinations of
points):
q1 = (11/13)c1 + (3/13)c2 -(3/13)c3 + (2/13)c4
q2 = -c1 + (3/2)c2 + (3/2)c3 - c4
q3 = (2/13)c1 - (3/13)c2 + (3/13)c3 + (11/13)c4
Of course, this curve does not interpolate the end-points, but it would
be interesting to see the behaviour of such a curve in an applet.
--
Kalle Rutanen
http://kaba.hilvi.org
*/
// reduce to a quadratic or smaller
// look for identical points
// look for all four points in a line
// note that three points in a line doesn't simplify a cubic
// look for approximation with single quadratic
// save approximation with multiple quadratics for later
int SkReduceOrder::reduce(
const SkDCubic& cubic, Quadratics allowQuadratics) {
int index, minX, maxX, minY, maxY;
int minXSet, minYSet;
minX = maxX = minY = maxY = 0;
minXSet = minYSet = 0;
for (index = 1; index < 4; ++index) {
if (cubic[minX].fX > cubic[index].fX) {
minX = index;
}
if (cubic[minY].fY > cubic[index].fY) {
minY = index;
}
if (cubic[maxX].fX < cubic[index].fX) {
maxX = index;
}
if (cubic[maxY].fY < cubic[index].fY) {
maxY = index;
}
}
for (index = 0; index < 4; ++index) {
double cx = cubic[index].fX;
double cy = cubic[index].fY;
double denom = std::max(fabs(cx), std::max(fabs(cy),
std::max(fabs(cubic[minX].fX), fabs(cubic[minY].fY))));
if (denom == 0) {
minXSet |= 1 << index;
minYSet |= 1 << index;
continue;
}
double inv = 1 / denom;
if (approximately_equal_half(cx * inv, cubic[minX].fX * inv)) {
minXSet |= 1 << index;
}
if (approximately_equal_half(cy * inv, cubic[minY].fY * inv)) {
minYSet |= 1 << index;
}
}
if (minXSet == 0xF) {
// test for vertical line
if (minYSet == 0xF) {
// return 1 if all four are coincident
return coincident_line(cubic, fCubic);
}
return vertical_line(cubic, fCubic);
}
if (minYSet == 0xF) {
// test for horizontal line
return horizontal_line(cubic, fCubic);
}
int result = check_linear(cubic, minX, maxX, minY, maxY, fCubic);
if (result) {
return result;
}
if (allowQuadratics == SkReduceOrder::kAllow_Quadratics
&& (result = check_quadratic(cubic, fCubic))) {
return result;
}
fCubic = cubic;
return 4;
}
SkPath::Verb SkReduceOrder::Quad(
const SkPoint a[3], SkPoint* reducePts) {
SkDQuad quad;
quad.set(a);
SkReduceOrder reducer;
int order = reducer.reduce(quad);
if (order == 2) {
// quad became line
for (
int index = 0; index < order; ++index) {
*reducePts++ = reducer.fLine[index].asSkPoint();
}
}
return SkPathOpsPointsToVerb(order - 1);
}
SkPath::Verb SkReduceOrder::Conic(
const SkConic& c, SkPoint* reducePts) {
SkPath::Verb verb = SkReduceOrder::Quad(c.fPts, reducePts);
if (verb > SkPath::kLine_Verb && c.fW == 1) {
return SkPath::kQuad_Verb;
}
return verb == SkPath::kQuad_Verb ? SkPath::kConic_Verb : verb;
}
SkPath::Verb SkReduceOrder::Cubic(
const SkPoint a[4], SkPoint* reducePts) {
if (SkDPoint::ApproximatelyEqual(a[0], a[1]) && SkDPoint::ApproximatelyEqual(a[0], a[2]
)
&& SkDPoint::ApproximatelyEqual(a[0], a[3])) {
reducePts[0] = a[0];
return SkPath::kMove_Verb;
}
SkDCubic cubic;
cubic.set(a);
SkReduceOrder reducer;
int order = reducer.reduce(cubic, kAllow_Quadratics);
if (order == 2 || order == 3) { // cubic became line or quad
for (int index = 0; index < order; ++index) {
*reducePts++ = reducer.fQuad[index].asSkPoint();
}
}
return SkPathOpsPointsToVerb(order - 1);
}
