michael@0: /*
michael@0:  * Copyright 2012 Google Inc.
michael@0:  *
michael@0:  * Use of this source code is governed by a BSD-style license that can be
michael@0:  * found in the LICENSE file.
michael@0:  */
michael@0: #include "SkPathOpsLine.h"
michael@0: 
michael@0: SkDLine SkDLine::subDivide(double t1, double t2) const {
michael@0:     SkDVector delta = tangent();
michael@0:     SkDLine dst = {{{
michael@0:             fPts[0].fX - t1 * delta.fX, fPts[0].fY - t1 * delta.fY}, {
michael@0:             fPts[0].fX - t2 * delta.fX, fPts[0].fY - t2 * delta.fY}}};
michael@0:     return dst;
michael@0: }
michael@0: 
michael@0: // may have this below somewhere else already:
michael@0: // copying here because I thought it was clever
michael@0: 
michael@0: // Copyright 2001, softSurfer (www.softsurfer.com)
michael@0: // This code may be freely used and modified for any purpose
michael@0: // providing that this copyright notice is included with it.
michael@0: // SoftSurfer makes no warranty for this code, and cannot be held
michael@0: // liable for any real or imagined damage resulting from its use.
michael@0: // Users of this code must verify correctness for their application.
michael@0: 
michael@0: // Assume that a class is already given for the object:
michael@0: //    Point with coordinates {float x, y;}
michael@0: //===================================================================
michael@0: 
michael@0: // isLeft(): tests if a point is Left|On|Right of an infinite line.
michael@0: //    Input:  three points P0, P1, and P2
michael@0: //    Return: >0 for P2 left of the line through P0 and P1
michael@0: //            =0 for P2 on the line
michael@0: //            <0 for P2 right of the line
michael@0: //    See: the January 2001 Algorithm on Area of Triangles
michael@0: //    return (float) ((P1.x - P0.x)*(P2.y - P0.y) - (P2.x - P0.x)*(P1.y - P0.y));
michael@0: double SkDLine::isLeft(const SkDPoint& pt) const {
michael@0:     SkDVector p0 = fPts[1] - fPts[0];
michael@0:     SkDVector p2 = pt - fPts[0];
michael@0:     return p0.cross(p2);
michael@0: }
michael@0: 
michael@0: SkDPoint SkDLine::ptAtT(double t) const {
michael@0:     if (0 == t) {
michael@0:         return fPts[0];
michael@0:     }
michael@0:     if (1 == t) {
michael@0:         return fPts[1];
michael@0:     }
michael@0:     double one_t = 1 - t;
michael@0:     SkDPoint result = { one_t * fPts[0].fX + t * fPts[1].fX, one_t * fPts[0].fY + t * fPts[1].fY };
michael@0:     return result;
michael@0: }
michael@0: 
michael@0: double SkDLine::exactPoint(const SkDPoint& xy) const {
michael@0:     if (xy == fPts[0]) {  // do cheapest test first
michael@0:         return 0;
michael@0:     }
michael@0:     if (xy == fPts[1]) {
michael@0:         return 1;
michael@0:     }
michael@0:     return -1;
michael@0: }
michael@0: 
michael@0: double SkDLine::nearPoint(const SkDPoint& xy) const {
michael@0:     if (!AlmostBetweenUlps(fPts[0].fX, xy.fX, fPts[1].fX)
michael@0:             || !AlmostBetweenUlps(fPts[0].fY, xy.fY, fPts[1].fY)) {
michael@0:         return -1;
michael@0:     }
michael@0:     // project a perpendicular ray from the point to the line; find the T on the line
michael@0:     SkDVector len = fPts[1] - fPts[0]; // the x/y magnitudes of the line
michael@0:     double denom = len.fX * len.fX + len.fY * len.fY;  // see DLine intersectRay
michael@0:     SkDVector ab0 = xy - fPts[0];
michael@0:     double numer = len.fX * ab0.fX + ab0.fY * len.fY;
michael@0:     if (!between(0, numer, denom)) {
michael@0:         return -1;
michael@0:     }
michael@0:     double t = numer / denom;
michael@0:     SkDPoint realPt = ptAtT(t);
michael@0:     double dist = realPt.distance(xy);   // OPTIMIZATION: can we compare against distSq instead ?
michael@0:     // find the ordinal in the original line with the largest unsigned exponent
michael@0:     double tiniest = SkTMin(SkTMin(SkTMin(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
michael@0:     double largest = SkTMax(SkTMax(SkTMax(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
michael@0:     largest = SkTMax(largest, -tiniest);
michael@0:     if (!AlmostEqualUlps(largest, largest + dist)) { // is the dist within ULPS tolerance?
michael@0:         return -1;
michael@0:     }
michael@0:     t = SkPinT(t);
michael@0:     SkASSERT(between(0, t, 1));
michael@0:     return t;
michael@0: }
michael@0: 
michael@0: bool SkDLine::nearRay(const SkDPoint& xy) const {
michael@0:     // project a perpendicular ray from the point to the line; find the T on the line
michael@0:     SkDVector len = fPts[1] - fPts[0]; // the x/y magnitudes of the line
michael@0:     double denom = len.fX * len.fX + len.fY * len.fY;  // see DLine intersectRay
michael@0:     SkDVector ab0 = xy - fPts[0];
michael@0:     double numer = len.fX * ab0.fX + ab0.fY * len.fY;
michael@0:     double t = numer / denom;
michael@0:     SkDPoint realPt = ptAtT(t);
michael@0:     double dist = realPt.distance(xy);   // OPTIMIZATION: can we compare against distSq instead ?
michael@0:     // find the ordinal in the original line with the largest unsigned exponent
michael@0:     double tiniest = SkTMin(SkTMin(SkTMin(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
michael@0:     double largest = SkTMax(SkTMax(SkTMax(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
michael@0:     largest = SkTMax(largest, -tiniest);
michael@0:     return RoughlyEqualUlps(largest, largest + dist); // is the dist within ULPS tolerance?
michael@0: }
michael@0: 
michael@0: // Returns true if a ray from (0,0) to (x1,y1) is coincident with a ray (0,0) to (x2,y2)
michael@0: // OPTIMIZE: a specialty routine could speed this up -- may not be called very often though
michael@0: bool SkDLine::NearRay(double x1, double y1, double x2, double y2) {
michael@0:     double denom1 = x1 * x1 + y1 * y1;
michael@0:     double denom2 = x2 * x2 + y2 * y2;
michael@0:     SkDLine line = {{{0, 0}, {x1, y1}}};
michael@0:     SkDPoint pt = {x2, y2};
michael@0:     if (denom2 > denom1) {
michael@0:         SkTSwap(line[1], pt);
michael@0:     }
michael@0:     return line.nearRay(pt);
michael@0: }
michael@0: 
michael@0: double SkDLine::ExactPointH(const SkDPoint& xy, double left, double right, double y) {
michael@0:     if (xy.fY == y) {
michael@0:         if (xy.fX == left) {
michael@0:             return 0;
michael@0:         }
michael@0:         if (xy.fX == right) {
michael@0:             return 1;
michael@0:         }
michael@0:     }
michael@0:     return -1;
michael@0: }
michael@0: 
michael@0: double SkDLine::NearPointH(const SkDPoint& xy, double left, double right, double y) {
michael@0:     if (!AlmostBequalUlps(xy.fY, y)) {
michael@0:         return -1;
michael@0:     }
michael@0:     if (!AlmostBetweenUlps(left, xy.fX, right)) {
michael@0:         return -1;
michael@0:     }
michael@0:     double t = (xy.fX - left) / (right - left);
michael@0:     t = SkPinT(t);
michael@0:     SkASSERT(between(0, t, 1));
michael@0:     double realPtX = (1 - t) * left + t * right;
michael@0:     SkDVector distU = {xy.fY - y, xy.fX - realPtX};
michael@0:     double distSq = distU.fX * distU.fX + distU.fY * distU.fY;
michael@0:     double dist = sqrt(distSq); // OPTIMIZATION: can we compare against distSq instead ?
michael@0:     double tiniest = SkTMin(SkTMin(y, left), right);
michael@0:     double largest = SkTMax(SkTMax(y, left), right);
michael@0:     largest = SkTMax(largest, -tiniest);
michael@0:     if (!AlmostEqualUlps(largest, largest + dist)) { // is the dist within ULPS tolerance?
michael@0:         return -1;
michael@0:     }
michael@0:     return t;
michael@0: }
michael@0: 
michael@0: double SkDLine::ExactPointV(const SkDPoint& xy, double top, double bottom, double x) {
michael@0:     if (xy.fX == x) {
michael@0:         if (xy.fY == top) {
michael@0:             return 0;
michael@0:         }
michael@0:         if (xy.fY == bottom) {
michael@0:             return 1;
michael@0:         }
michael@0:     }
michael@0:     return -1;
michael@0: }
michael@0: 
michael@0: double SkDLine::NearPointV(const SkDPoint& xy, double top, double bottom, double x) {
michael@0:     if (!AlmostBequalUlps(xy.fX, x)) {
michael@0:         return -1;
michael@0:     }
michael@0:     if (!AlmostBetweenUlps(top, xy.fY, bottom)) {
michael@0:         return -1;
michael@0:     }
michael@0:     double t = (xy.fY - top) / (bottom - top);
michael@0:     t = SkPinT(t);
michael@0:     SkASSERT(between(0, t, 1));
michael@0:     double realPtY = (1 - t) * top + t * bottom;
michael@0:     SkDVector distU = {xy.fX - x, xy.fY - realPtY};
michael@0:     double distSq = distU.fX * distU.fX + distU.fY * distU.fY;
michael@0:     double dist = sqrt(distSq); // OPTIMIZATION: can we compare against distSq instead ?
michael@0:     double tiniest = SkTMin(SkTMin(x, top), bottom);
michael@0:     double largest = SkTMax(SkTMax(x, top), bottom);
michael@0:     largest = SkTMax(largest, -tiniest);
michael@0:     if (!AlmostEqualUlps(largest, largest + dist)) { // is the dist within ULPS tolerance?
michael@0:         return -1;
michael@0:     }
michael@0:     return t;
michael@0: }
michael@0: 
michael@0: #ifdef SK_DEBUG
michael@0: void SkDLine::dump() {
michael@0:     SkDebugf("{{");
michael@0:     fPts[0].dump();
michael@0:     SkDebugf(", ");
michael@0:     fPts[1].dump();
michael@0:     SkDebugf("}}\n");
michael@0: }
michael@0: #endif