/*
* 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 "CurveIntersection.h"
#include "Intersection_Tests.h"
#include "IntersectionUtilities.h"
const Cubic convex[] = {
{{0, 0}, {2, 0}, {2, 1}, {0, 1}},
{{1, 0}, {1, 1}, {0, 1}, {0, 0}},
{{1, 1}, {0, 1}, {0, 0}, {1, 0}},
{{0, 1}, {0, 0}, {1, 0}, {1, 1}},
{{0, 0}, {10, 0}, {10, 10}, {5, 6}},
};
size_t convex_count = sizeof(convex) / sizeof(convex[0]);
const Cubic bowtie[] = {
{{0, 0}, {1, 1}, {1, 0}, {0, 1}},
{{1, 0}, {0, 1}, {1, 1}, {0, 0}},
{{1, 1}, {0, 0}, {0, 1}, {1, 0}},
{{0, 1}, {1, 0}, {0, 0}, {1, 1}},
};
size_t bowtie_count = sizeof(bowtie) / sizeof(bowtie[0]);
const Cubic arrow[] = {
{{0, 0}, {10, 0}, {10, 10}, {5, 4}},
{{10, 0}, {10, 10}, {5, 4}, {0, 0}},
{{10, 10}, {5, 4}, {0, 0}, {10, 0}},
{{5, 4}, {0, 0}, {10, 0}, {10, 10}},
};
size_t arrow_count = sizeof(arrow) / sizeof(arrow[0]);
const Cubic three[] = {
{{1, 0}, {1, 0}, {1, 1}, {0, 1}}, // 0 == 1
{{0, 0}, {1, 1}, {1, 1}, {0, 1}}, // 1 == 2
{{0, 0}, {1, 0}, {0, 1}, {0, 1}}, // 2 == 3
{{1, 0}, {1, 1}, {1, 0}, {0, 1}}, // 0 == 2
{{1, 0}, {1, 1}, {0, 1}, {1, 0}}, // 0 == 3
{{0, 0}, {1, 0}, {1, 1}, {1, 0}}, // 1 == 3
};
size_t three_count = sizeof(three) / sizeof(three[0]);
const Cubic triangle[] = {
{{0, 0}, {1, 0}, {2, 0}, {0, 1}}, // extra point on horz
{{1, 0}, {2, 0}, {0, 1}, {0, 0}},
{{2, 0}, {0, 1}, {0, 0}, {1, 0}},
{{0, 1}, {0, 0}, {1, 0}, {2, 0}},
{{0, 0}, {0, 1}, {0, 2}, {1, 1}}, // extra point on vert
{{0, 1}, {0, 2}, {1, 1}, {0, 0}},
{{0, 2}, {1, 1}, {0, 0}, {0, 1}},
{{1, 1}, {0, 0}, {0, 1}, {0, 2}},
{{0, 0}, {1, 1}, {2, 2}, {2, 0}}, // extra point on diag
{{1, 1}, {2, 2}, {2, 0}, {0, 0}},
{{2, 2}, {2, 0}, {0, 0}, {1, 1}},
{{2, 0}, {0, 0}, {1, 1}, {2, 2}},
{{0, 0}, {2, 0}, {2, 2}, {1, 1}}, // extra point on diag
{{2, 0}, {2, 2}, {1, 1}, {0, 0}},
{{2, 2}, {1, 1}, {0, 0}, {2, 0}},
{{1, 1}, {0, 0}, {2, 0}, {2, 2}},
};
size_t triangle_count = sizeof(triangle) / sizeof(triangle[0]);
const struct CubicDataSet {
const Cubic* data;
size_t size;
} cubicDataSet[] = {
{ three, three_count },
{ convex, convex_count },
{ bowtie, bowtie_count },
{ arrow, arrow_count },
{ triangle, triangle_count },
};
size_t cubicDataSet_count = sizeof(cubicDataSet) / sizeof(cubicDataSet[0]);
typedef double Matrix3x2[3][2];
static bool rotateToAxis(const _Point& a, const _Point& b, Matrix3x2& matrix) {
double dx = b.x - a.x;
double dy = b.y - a.y;
double length = sqrt(dx * dx + dy * dy);
if (length == 0) {
return false;
}
double invLength = 1 / length;
matrix[0][0] = dx * invLength;
matrix[1][0] = dy * invLength;
matrix[2][0] = 0;
matrix[0][1] = -dy * invLength;
matrix[1][1] = dx * invLength;
matrix[2][1] = 0;
return true;
}
static void transform(const Cubic& cubic, const Matrix3x2& matrix, Cubic& rotPath) {
for (int index = 0; index < 4; ++index) {
rotPath[index].x = cubic[index].x * matrix[0][0]
+ cubic[index].y * matrix[1][0] + matrix[2][0];
rotPath[index].y = cubic[index].x * matrix[0][1]
+ cubic[index].y * matrix[1][1] + matrix[2][1];
}
}
// brute force way to find convex hull:
// pick two points
// rotate all four until the two points are horizontal
// are the remaining two points both above or below the horizontal line?
// if so, the two points must be an edge of the convex hull
static int rotate_to_hull(const Cubic& cubic, char order[4], size_t idx, size_t inr) {
bool debug_rotate_to_hull = false;
int outsidePtSet[4];
memset(outsidePtSet, -1, sizeof(outsidePtSet));
for (int outer = 0; outer < 3; ++outer) {
for (int priorOuter = 0; priorOuter < outer; ++priorOuter) {
if (cubic[outer].approximatelyEqual(cubic[priorOuter])) {
goto skip;
}
}
for (int inner = outer + 1; inner < 4; ++inner) {
for (int priorInner = outer + 1; priorInner < inner; ++priorInner) {
if (cubic[inner].approximatelyEqual(cubic[priorInner])) {
goto skipInner;
}
}
if (cubic[outer].approximatelyEqual(cubic[inner])) {
continue;
}
Matrix3x2 matrix;
if (!rotateToAxis(cubic[outer], cubic[inner], matrix)) {
continue;
}
Cubic rotPath;
transform(cubic, matrix, rotPath);
int sides[3];
int zeroes;
zeroes = -1;
bzero(sides, sizeof(sides));
if (debug_rotate_to_hull) SkDebugf("%s [%d,%d] [o=%d,i=%d] src=(%g,%g) rot=", __FUNCTION__,
(int)idx, (int)inr, (int)outer, (int)inner,
cubic[inner].x, cubic[inner].y);
for (int index = 0; index < 4; ++index) {
if (debug_rotate_to_hull) SkDebugf("(%g,%g) ", rotPath[index].x, rotPath[index].y);
sides[side(rotPath[index].y - rotPath[inner].y)]++;
if (index != outer && index != inner
&& side(rotPath[index].y - rotPath[inner].y) == 1)
zeroes = index;
}
if (debug_rotate_to_hull) SkDebugf("sides=(%d,%d,%d)\n", sides[0], sides[1], sides[2]);
if (sides[0] && sides[2]) {
continue;
}
if (sides[1] == 3 && zeroes >= 0) {
// verify that third point is between outer, inner
// if either of remaining two equals outer or equal, pick lower
if (rotPath[zeroes].approximatelyEqual(rotPath[inner])
&& zeroes < inner) {
if (debug_rotate_to_hull) SkDebugf("%s [%d,%d] [o=%d,i=%d] zeroes < inner\n",
__FUNCTION__, (int)idx, (int)inr, (int)outer, (int)inner);
continue;
}
if (rotPath[zeroes].approximatelyEqual(rotPath[outer])
&& zeroes < outer) {
if (debug_rotate_to_hull) SkDebugf("%s [%d,%d] [o=%d,i=%d] zeroes < outer\n",
__FUNCTION__, (int)idx, (int)inr, (int)outer, (int)inner);
continue;
}
if (rotPath[zeroes].x < rotPath[inner].x
&& rotPath[zeroes].x < rotPath[outer].x) {
if (debug_rotate_to_hull) SkDebugf("%s [%d,%d] [o=%d,i=%d] zeroes < inner && outer\n",
__FUNCTION__, (int)idx, (int)inr, (int)outer, (int)inner);
continue;
}
if (rotPath[zeroes].x > rotPath[inner].x
&& rotPath[zeroes].x > rotPath[outer].x) {
if (debug_rotate_to_hull) SkDebugf("%s [%d,%d] [o=%d,i=%d] zeroes > inner && outer\n",
__FUNCTION__, (int)idx, (int)inr, (int)outer, (int)inner);
continue;
}
}
if (outsidePtSet[outer] < 0) {
outsidePtSet[outer] = inner;
} else {
if (outsidePtSet[inner] > 0) {
if (debug_rotate_to_hull) SkDebugf("%s [%d,%d] [o=%d,i=%d] too many rays from one point\n",
__FUNCTION__, (int)idx, (int)inr, (int)outer, (int)inner);
}
outsidePtSet[inner] = outer;
}
skipInner:
;
}
skip:
;
}
int totalSides = 0;
int first = 0;
for (; first < 4; ++first) {
if (outsidePtSet[first] >= 0) {
break;
}
}
if (first > 3) {
order[0] = 0;
return 1;
}
int next = first;
do {
order[totalSides++] = next;
next = outsidePtSet[next];
} while (next != -1 && next != first);
return totalSides;
}
int firstIndex = 0;
int firstInner = 0;
void ConvexHull_Test() {
for (size_t index = firstIndex; index < cubicDataSet_count; ++index) {
const CubicDataSet& set = cubicDataSet[index];
for (size_t inner = firstInner; inner < set.size; ++inner) {
const Cubic& cubic = set.data[inner];
char order[4], cmpOrder[4];
int cmp = rotate_to_hull(cubic, cmpOrder, index, inner);
if (cmp < 3) {
continue;
}
int result = convex_hull(cubic, order);
if (cmp != result) {
SkDebugf("%s [%d,%d] result=%d cmp=%d\n", __FUNCTION__,
(int)index, (int)inner, result, cmp);
continue;
}
// check for same indices
char pts = 0;
char cmpPts = 0;
int pt, bit;
for (pt = 0; pt < cmp; ++pt) {
if (pts & 1 << order[pt]) {
SkDebugf("%s [%d,%d] duplicate index in order: %d,%d,%d",
__FUNCTION__, (int)index, (int)inner,
order[0], order[1], order[2]);
if (cmp == 4) {
SkDebugf(",%d", order[3]);
}
SkDebugf("\n");
goto next;
}
if (cmpPts & 1 << cmpOrder[pt]) {
SkDebugf("%s [%d,%d] duplicate index in order: %d,%d,%d",
__FUNCTION__, (int)index, (int)inner,
cmpOrder[0], cmpOrder[1], cmpOrder[2]);
if (cmp == 4) {
SkDebugf(",%d", cmpOrder[3]);
}
SkDebugf("\n");
goto next;
}
pts |= 1 << order[pt];
cmpPts |= 1 << cmpOrder[pt];
}
for (bit = 0; bit < 4; ++bit) {
if (pts & 1 << bit) {
continue;
}
for (pt = 0; pt < cmp; ++pt) {
if (order[pt] == bit) {
continue;
}
if (cubic[order[pt]] == cubic[bit]) {
pts |= 1 << bit;
}
}
}
for (bit = 0; bit < 4; ++bit) {
if (cmpPts & 1 << bit) {
continue;
}
for (pt = 0; pt < cmp; ++pt) {
if (cmpOrder[pt] == bit) {
continue;
}
if (cubic[cmpOrder[pt]] == cubic[bit]) {
cmpPts |= 1 << bit;
}
}
}
if (pts != cmpPts) {
SkDebugf("%s [%d,%d] mismatch indices: order=%d,%d,%d",
__FUNCTION__, (int)index, (int)inner,
order[0], order[1], order[2]);
if (cmp == 4) {
SkDebugf(",%d", order[3]);
}
SkDebugf(" cmpOrder=%d,%d,%d", cmpOrder[0], cmpOrder[1], cmpOrder[2]);
if (cmp == 4) {
SkDebugf(",%d", cmpOrder[3]);
}
SkDebugf("\n");
continue;
}
if (cmp == 4) { // check for bow ties
int match = 0;
while (cmpOrder[match] != order[0]) {
++match;
}
if (cmpOrder[match ^ 2] != order[2]) {
SkDebugf("%s [%d,%d] bowtie mismatch: order=%d,%d,%d,%d"
" cmpOrder=%d,%d,%d,%d\n",
__FUNCTION__, (int)index, (int)inner,
order[0], order[1], order[2], order[3],
cmpOrder[0], cmpOrder[1], cmpOrder[2], cmpOrder[3]);
}
}
next:
;
}
}
}
const double a = 1.0/3;
const double b = 2.0/3;
const Cubic x_cubic[] = {
{{0, 0}, {a, 0}, {b, 0}, {1, 0}}, // 0
{{0, 0}, {a, 0}, {b, 0}, {1, 1}}, // 1
{{0, 0}, {a, 0}, {b, 1}, {1, 0}}, // 2
{{0, 0}, {a, 0}, {b, 1}, {1, 1}}, // 3
{{0, 0}, {a, 1}, {b, 0}, {1, 0}}, // 4
{{0, 0}, {a, 1}, {b, 0}, {1, 1}}, // 5
{{0, 0}, {a, 1}, {b, 1}, {1, 0}}, // 6
{{0, 0}, {a, 1}, {b, 1}, {1, 1}}, // 7
{{0, 1}, {a, 0}, {b, 0}, {1, 0}}, // 8
{{0, 1}, {a, 0}, {b, 0}, {1, 1}}, // 9
{{0, 1}, {a, 0}, {b, 1}, {1, 0}}, // 10
{{0, 1}, {a, 0}, {b, 1}, {1, 1}}, // 11
{{0, 1}, {a, 1}, {b, 0}, {1, 0}}, // 12
{{0, 1}, {a, 1}, {b, 0}, {1, 1}}, // 13
{{0, 1}, {a, 1}, {b, 1}, {1, 0}}, // 14
{{0, 1}, {a, 1}, {b, 1}, {1, 1}}, // 15
};
size_t x_cubic_count = sizeof(x_cubic) / sizeof(x_cubic[0]);
static int first_x_test = 0;
void ConvexHull_X_Test() {
for (size_t index = first_x_test; index < x_cubic_count; ++index) {
const Cubic& cubic = x_cubic[index];
char connectTo0[2] = {-1, -1};
char connectTo3[2] = {-1, -1};
convex_x_hull(cubic, connectTo0, connectTo3);
int idx, cmp;
for (idx = 0; idx < 2; ++idx) {
if (connectTo0[idx] >= 1 && connectTo0[idx] < 4) {
continue;
} else {
SkDebugf("%s connectTo0[idx]=%d", __FUNCTION__, connectTo0[idx]);
}
if (connectTo3[idx] >= 0 && connectTo3[idx] < 3) {
continue;
} else {
SkDebugf("%s connectTo3[idx]=%d", __FUNCTION__, connectTo3[idx]);
}
goto nextTest;
}
char rOrder[4];
char cmpOrder[4];
cmp = rotate_to_hull(cubic, cmpOrder, index, 0);
if (index == 0 || index == 15) {
// FIXME: make rotate_to_hull work for degenerate 2 edge hull cases
cmpOrder[0] = 0;
cmpOrder[1] = 3;
cmp = 2;
}
if (cmp < 3) {
// FIXME: make rotate_to_hull work for index == 3 etc
continue;
}
for (idx = 0; idx < cmp; ++idx) {
if (cmpOrder[idx] == 0) {
rOrder[0] = cmpOrder[(idx + 1) % cmp];
rOrder[1] = cmpOrder[(idx + cmp - 1) % cmp];
} else if (cmpOrder[idx] == 3) {
rOrder[2] = cmpOrder[(idx + 1) % cmp];
rOrder[3] = cmpOrder[(idx + cmp - 1) % cmp];
}
}
if (connectTo0[0] != connectTo0[1]) {
if (rOrder[0] == rOrder[1]) {
SkDebugf("%s [%d] (1) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
__FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
connectTo3[0], connectTo3[1],
rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
continue;
}
int unused = 6 - connectTo0[0] - connectTo0[1];
int rUnused = 6 - rOrder[0] - rOrder[1];
if (unused != rUnused) {
SkDebugf("%s [%d] (2) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
__FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
connectTo3[0], connectTo3[1],
rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
continue;
}
} else {
if (rOrder[0] != rOrder[1]) {
SkDebugf("%s [%d] (3) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
__FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
connectTo3[0], connectTo3[1],
rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
continue;
}
if (connectTo0[0] != rOrder[0]) {
SkDebugf("%s [%d] (4) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
__FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
connectTo3[0], connectTo3[1],
rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
continue;
}
}
if (connectTo3[0] != connectTo3[1]) {
if (rOrder[2] == rOrder[3]) {
SkDebugf("%s [%d] (5) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
__FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
connectTo3[0], connectTo3[1],
rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
continue;
}
int unused = 6 - connectTo3[0] - connectTo3[1];
int rUnused = 6 - rOrder[2] - rOrder[3];
if (unused != rUnused) {
SkDebugf("%s [%d] (6) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
__FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
connectTo3[0], connectTo3[1],
rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
continue;
}
} else {
if (rOrder[2] != rOrder[3]) {
SkDebugf("%s [%d] (7) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
__FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
connectTo3[0], connectTo3[1],
rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
continue;
}
if (connectTo3[1] != rOrder[3]) {
SkDebugf("%s [%d] (8) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
__FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
connectTo3[0], connectTo3[1],
rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
continue;
}
}
nextTest:
;
}
}