src/pathops/SkReduceOrder.cpp - skia - Git at Google

 /*
  * 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 "SkGeometry.h"
 #include "SkReduceOrder.h"

 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 = SkTMax(fabs(cx), SkTMax(fabs(cy),
                 SkTMax(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);
 }
	/*
	* 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 "SkGeometry.h"
	#include "SkReduceOrder.h"

	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 = SkTMax(fabs(cx), SkTMax(fabs(cy),
	SkTMax(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);
	}