From 07dc6d2b450e7931c6f6970eb6cde600b28a99e2 Mon Sep 17 00:00:00 2001 From: Dmitry Kurtaev Date: Mon, 30 Apr 2018 21:51:33 +0300 Subject: [PATCH] Return a convex hull from rotatedRectangleIntersection --- modules/dnn/src/nms.cpp | 5 +- modules/imgproc/src/intersection.cpp | 14 +- modules/imgproc/test/test_intersection.cpp | 459 ++++++++------------- samples/dnn/text_detection.cpp | 22 +- 4 files changed, 188 insertions(+), 312 deletions(-) diff --git a/modules/dnn/src/nms.cpp b/modules/dnn/src/nms.cpp index 2ce1257cad..62bda79c15 100644 --- a/modules/dnn/src/nms.cpp +++ b/modules/dnn/src/nms.cpp @@ -32,14 +32,13 @@ void NMSBoxes(const std::vector& bboxes, const std::vector& scores, static inline float rotatedRectIOU(const RotatedRect& a, const RotatedRect& b) { - std::vector inter, hull; + std::vector inter; int res = rotatedRectangleIntersection(a, b, inter); if (inter.empty() || res == INTERSECT_NONE) return 0.0f; if (res == INTERSECT_FULL) return 1.0f; - convexHull(inter, hull); - float interArea = contourArea(hull); + float interArea = contourArea(inter); return interArea / (a.size.area() + b.size.area() - interArea); } diff --git a/modules/imgproc/src/intersection.cpp b/modules/imgproc/src/intersection.cpp index 5da743a0f9..3e4a266b30 100644 --- a/modules/imgproc/src/intersection.cpp +++ b/modules/imgproc/src/intersection.cpp @@ -219,13 +219,15 @@ int rotatedRectangleIntersection( const RotatedRect& rect1, const RotatedRect& r } } - // Get rid of dupes + // Get rid of dupes and order points. for( int i = 0; i < (int)intersection.size()-1; i++ ) { + float dx1 = intersection[i + 1].x - intersection[i].x; + float dy1 = intersection[i + 1].y - intersection[i].y; for( size_t j = i+1; j < intersection.size(); j++ ) { - float dx = intersection[i].x - intersection[j].x; - float dy = intersection[i].y - intersection[j].y; + float dx = intersection[j].x - intersection[i].x; + float dy = intersection[j].y - intersection[i].y; double d2 = dx*dx + dy*dy; // can be a really small number, need double here if( d2 < samePointEps*samePointEps ) @@ -235,6 +237,12 @@ int rotatedRectangleIntersection( const RotatedRect& rect1, const RotatedRect& r intersection.pop_back(); j--; // restart check } + else if (dx1 * dy - dy1 * dx < 0) + { + std::swap(intersection[i + 1], intersection[j]); + dx1 = dx; + dy1 = dy; + } } } diff --git a/modules/imgproc/test/test_intersection.cpp b/modules/imgproc/test/test_intersection.cpp index e2d8f18e33..8d770d06ea 100644 --- a/modules/imgproc/test/test_intersection.cpp +++ b/modules/imgproc/test/test_intersection.cpp @@ -66,8 +66,27 @@ private: void test7(); void test8(); void test9(); + void test10(); + void test11(); + void test12(); + void test13(); + void test14(); }; +static void compare(const std::vector& test, const std::vector& target) +{ + ASSERT_EQ(test.size(), target.size()); + ASSERT_TRUE(test.size() < 4 || isContourConvex(test)); + ASSERT_TRUE(target.size() < 4 || isContourConvex(target)); + for( size_t i = 0; i < test.size(); i++ ) + { + double dx = test[i].x - target[i].x; + double dy = test[i].y - target[i].y; + double r = sqrt(dx*dx + dy*dy); + ASSERT_LT(r, ACCURACY); + } +} + void CV_RotatedRectangleIntersectionTest::run(int) { // See pics/intersection.png for the scenarios we are testing @@ -92,28 +111,20 @@ void CV_RotatedRectangleIntersectionTest::run(int) test7(); test8(); test9(); + test10(); + test11(); + test12(); + test13(); + test14(); } void CV_RotatedRectangleIntersectionTest::test1() { // no intersection - - RotatedRect rect1, rect2; - - rect1.center.x = 0; - rect1.center.y = 0; - rect1.size.width = 2; - rect1.size.height = 2; - rect1.angle = 12.0f; - - rect2.center.x = 10; - rect2.center.y = 10; - rect2.size.width = 2; - rect2.size.height = 2; - rect2.angle = 34.0f; + RotatedRect rect1(Point2f(0, 0), Size2f(2, 2), 12.0f); + RotatedRect rect2(Point2f(10, 10), Size2f(2, 2), 34.0f); vector vertices; - int ret = rotatedRectangleIntersection(rect1, rect2, vertices); CV_Assert(ret == INTERSECT_NONE); @@ -123,375 +134,243 @@ void CV_RotatedRectangleIntersectionTest::test1() void CV_RotatedRectangleIntersectionTest::test2() { // partial intersection, rectangles translated - - RotatedRect rect1, rect2; - - rect1.center.x = 0; - rect1.center.y = 0; - rect1.size.width = 2; - rect1.size.height = 2; - rect1.angle = 0; - - rect2.center.x = 1; - rect2.center.y = 1; - rect2.size.width = 2; - rect2.size.height = 2; - rect2.angle = 0; + RotatedRect rect1(Point2f(0, 0), Size2f(2, 2), 0.0f); + RotatedRect rect2(Point2f(1, 1), Size2f(2, 2), 0.0f); vector vertices; - int ret = rotatedRectangleIntersection(rect1, rect2, vertices); CV_Assert(ret == INTERSECT_PARTIAL); - CV_Assert(vertices.size() == 4); - - vector possibleVertices(4); - possibleVertices[0] = Point2f(0.0f, 0.0f); - possibleVertices[1] = Point2f(1.0f, 1.0f); - possibleVertices[2] = Point2f(0.0f, 1.0f); - possibleVertices[3] = Point2f(1.0f, 0.0f); - - for( size_t i = 0; i < vertices.size(); i++ ) - { - double bestR = DBL_MAX; - - for( size_t j = 0; j < possibleVertices.size(); j++ ) - { - double dx = vertices[i].x - possibleVertices[j].x; - double dy = vertices[i].y - possibleVertices[j].y; - double r = sqrt(dx*dx + dy*dy); - - bestR = std::min(bestR, r); - } - - CV_Assert(bestR < ACCURACY); - } + vector targetVertices(4); + targetVertices[0] = Point2f(1.0f, 0.0f); + targetVertices[1] = Point2f(1.0f, 1.0f); + targetVertices[2] = Point2f(0.0f, 1.0f); + targetVertices[3] = Point2f(0.0f, 0.0f); + compare(vertices, targetVertices); } void CV_RotatedRectangleIntersectionTest::test3() { // partial intersection, rectangles rotated 45 degree on the corner, forms a triangle intersection - RotatedRect rect1, rect2; - - rect1.center.x = 0; - rect1.center.y = 0; - rect1.size.width = 2; - rect1.size.height = 2; - rect1.angle = 0; - - rect2.center.x = 1; - rect2.center.y = 1; - rect2.size.width = sqrt(2.0f); - rect2.size.height = 20; - rect2.angle = 45.0f; + RotatedRect rect1(Point2f(0, 0), Size2f(2, 2), 0.0f); + RotatedRect rect2(Point2f(1, 1), Size2f(sqrt(2.0f), 20), 45.0f); vector vertices; - int ret = rotatedRectangleIntersection(rect1, rect2, vertices); CV_Assert(ret == INTERSECT_PARTIAL); - CV_Assert(vertices.size() == 3); - - vector possibleVertices(3); - - possibleVertices[0] = Point2f(1.0f, 1.0f); - possibleVertices[1] = Point2f(0.0f, 1.0f); - possibleVertices[2] = Point2f(1.0f, 0.0f); - - for( size_t i = 0; i < vertices.size(); i++ ) - { - double bestR = DBL_MAX; - - for( size_t j = 0; j < possibleVertices.size(); j++ ) - { - double dx = vertices[i].x - possibleVertices[j].x; - double dy = vertices[i].y - possibleVertices[j].y; - double r = sqrt(dx*dx + dy*dy); - bestR = std::min(bestR, r); - } - - CV_Assert(bestR < ACCURACY); - } + vector targetVertices(3); + targetVertices[0] = Point2f(1.0f, 0.0f); + targetVertices[1] = Point2f(1.0f, 1.0f); + targetVertices[2] = Point2f(0.0f, 1.0f); + compare(vertices, targetVertices); } void CV_RotatedRectangleIntersectionTest::test4() { // full intersection, rectangles of same size directly on top of each other - - RotatedRect rect1, rect2; - - rect1.center.x = 0; - rect1.center.y = 0; - rect1.size.width = 2; - rect1.size.height = 2; - rect1.angle = 0; - - rect2.center.x = 0; - rect2.center.y = 0; - rect2.size.width = 2; - rect2.size.height = 2; - rect2.angle = 0; + RotatedRect rect1(Point2f(0, 0), Size2f(2, 2), 0.0f); + RotatedRect rect2(Point2f(0, 0), Size2f(2, 2), 0.0f); vector vertices; - int ret = rotatedRectangleIntersection(rect1, rect2, vertices); CV_Assert(ret == INTERSECT_FULL); - CV_Assert(vertices.size() == 4); - - vector possibleVertices(4); - - possibleVertices[0] = Point2f(-1.0f, 1.0f); - possibleVertices[1] = Point2f(1.0f, -1.0f); - possibleVertices[2] = Point2f(-1.0f, -1.0f); - possibleVertices[3] = Point2f(1.0f, 1.0f); - - for( size_t i = 0; i < vertices.size(); i++ ) - { - double bestR = DBL_MAX; - - for( size_t j = 0; j < possibleVertices.size(); j++ ) - { - double dx = vertices[i].x - possibleVertices[j].x; - double dy = vertices[i].y - possibleVertices[j].y; - double r = sqrt(dx*dx + dy*dy); - - bestR = std::min(bestR, r); - } - CV_Assert(bestR < ACCURACY); - } + vector targetVertices(4); + targetVertices[0] = Point2f(-1.0f, 1.0f); + targetVertices[1] = Point2f(-1.0f, -1.0f); + targetVertices[2] = Point2f(1.0f, -1.0f); + targetVertices[3] = Point2f(1.0f, 1.0f); + compare(vertices, targetVertices); } void CV_RotatedRectangleIntersectionTest::test5() { // partial intersection, rectangle on top rotated 45 degrees - - RotatedRect rect1, rect2; - - rect1.center.x = 0; - rect1.center.y = 0; - rect1.size.width = 2; - rect1.size.height = 2; - rect1.angle = 0; - - rect2.center.x = 0; - rect2.center.y = 0; - rect2.size.width = 2; - rect2.size.height = 2; - rect2.angle = 45.0f; + RotatedRect rect1(Point2f(0, 0), Size2f(2, 2), 0.0f); + RotatedRect rect2(Point2f(0, 0), Size2f(2, 2), 45.0f); vector vertices; - int ret = rotatedRectangleIntersection(rect1, rect2, vertices); CV_Assert(ret == INTERSECT_PARTIAL); - CV_Assert(vertices.size() == 8); - - vector possibleVertices(8); - possibleVertices[0] = Point2f(-1.0f, -0.414214f); - possibleVertices[1] = Point2f(-1.0f, 0.414214f); - possibleVertices[2] = Point2f(-0.414214f, -1.0f); - possibleVertices[3] = Point2f(0.414214f, -1.0f); - possibleVertices[4] = Point2f(1.0f, -0.414214f); - possibleVertices[5] = Point2f(1.0f, 0.414214f); - possibleVertices[6] = Point2f(0.414214f, 1.0f); - possibleVertices[7] = Point2f(-0.414214f, 1.0f); - - for( size_t i = 0; i < vertices.size(); i++ ) - { - double bestR = DBL_MAX; - - for( size_t j = 0; j < possibleVertices.size(); j++ ) - { - double dx = vertices[i].x - possibleVertices[j].x; - double dy = vertices[i].y - possibleVertices[j].y; - double r = sqrt(dx*dx + dy*dy); - - bestR = std::min(bestR, r); - } - - CV_Assert(bestR < ACCURACY); - } + vector targetVertices(8); + targetVertices[0] = Point2f(-1.0f, -0.414214f); + targetVertices[1] = Point2f(-0.414214f, -1.0f); + targetVertices[2] = Point2f(0.414214f, -1.0f); + targetVertices[3] = Point2f(1.0f, -0.414214f); + targetVertices[4] = Point2f(1.0f, 0.414214f); + targetVertices[5] = Point2f(0.414214f, 1.0f); + targetVertices[6] = Point2f(-0.414214f, 1.0f); + targetVertices[7] = Point2f(-1.0f, 0.414214f); + compare(vertices, targetVertices); } void CV_RotatedRectangleIntersectionTest::test6() { // 6 - partial intersection, rectangle on top of different size - - RotatedRect rect1, rect2; - - rect1.center.x = 0; - rect1.center.y = 0; - rect1.size.width = 2; - rect1.size.height = 2; - rect1.angle = 0; - - rect2.center.x = 0; - rect2.center.y = 0; - rect2.size.width = 2; - rect2.size.height = 10; - rect2.angle = 0; + RotatedRect rect1(Point2f(0, 0), Size2f(2, 2), 0.0f); + RotatedRect rect2(Point2f(0, 0), Size2f(2, 10), 0.0f); vector vertices; - int ret = rotatedRectangleIntersection(rect1, rect2, vertices); CV_Assert(ret == INTERSECT_PARTIAL); - CV_Assert(vertices.size() == 4); - - vector possibleVertices(4); - possibleVertices[0] = Point2f(1.0f, 1.0f); - possibleVertices[1] = Point2f(1.0f, -1.0f); - possibleVertices[2] = Point2f(-1.0f, -1.0f); - possibleVertices[3] = Point2f(-1.0f, 1.0f); - - for( size_t i = 0; i < vertices.size(); i++ ) - { - double bestR = DBL_MAX; - - for( size_t j = 0; j < possibleVertices.size(); j++ ) - { - double dx = vertices[i].x - possibleVertices[j].x; - double dy = vertices[i].y - possibleVertices[j].y; - double r = sqrt(dx*dx + dy*dy); - - bestR = std::min(bestR, r); - } - - CV_Assert(bestR < ACCURACY); - } + vector targetVertices(4); + targetVertices[0] = Point2f(-1.0f, -1.0f); + targetVertices[1] = Point2f(1.0f, -1.0f); + targetVertices[2] = Point2f(1.0f, 1.0f); + targetVertices[3] = Point2f(-1.0f, 1.0f); + compare(vertices, targetVertices); } void CV_RotatedRectangleIntersectionTest::test7() { // full intersection, rectangle fully enclosed in the other - - RotatedRect rect1, rect2; - - rect1.center.x = 0; - rect1.center.y = 0; - rect1.size.width = 12.34f; - rect1.size.height = 56.78f; - rect1.angle = 0; - - rect2.center.x = 0; - rect2.center.y = 0; - rect2.size.width = 2; - rect2.size.height = 2; - rect2.angle = 0; + RotatedRect rect1(Point2f(0, 0), Size2f(12.34f, 56.78f), 0.0f); + RotatedRect rect2(Point2f(0, 0), Size2f(2, 2), 0.0f); vector vertices; - int ret = rotatedRectangleIntersection(rect1, rect2, vertices); CV_Assert(ret == INTERSECT_FULL); - CV_Assert(vertices.size() == 4); - - vector possibleVertices(4); - possibleVertices[0] = Point2f(1.0f, 1.0f); - possibleVertices[1] = Point2f(1.0f, -1.0f); - possibleVertices[2] = Point2f(-1.0f, -1.0f); - possibleVertices[3] = Point2f(-1.0f, 1.0f); - - for( size_t i = 0; i < vertices.size(); i++ ) - { - double bestR = DBL_MAX; + vector targetVertices(4); + targetVertices[0] = Point2f(-1.0f, 1.0f); + targetVertices[1] = Point2f(-1.0f, -1.0f); + targetVertices[2] = Point2f(1.0f, -1.0f); + targetVertices[3] = Point2f(1.0f, 1.0f); + compare(vertices, targetVertices); +} - for( size_t j = 0; j < possibleVertices.size(); j++ ) - { - double dx = vertices[i].x - possibleVertices[j].x; - double dy = vertices[i].y - possibleVertices[j].y; - double r = sqrt(dx*dx + dy*dy); +void CV_RotatedRectangleIntersectionTest::test8() +{ + // intersection by a single vertex + RotatedRect rect1(Point2f(0, 0), Size2f(2, 2), 0.0f); + RotatedRect rect2(Point2f(2, 2), Size2f(2, 2), 0.0f); - bestR = std::min(bestR, r); - } + vector vertices; + int ret = rotatedRectangleIntersection(rect1, rect2, vertices); - CV_Assert(bestR < ACCURACY); - } + CV_Assert(ret == INTERSECT_PARTIAL); + compare(vertices, vector(1, Point2f(1.0f, 1.0f))); } -void CV_RotatedRectangleIntersectionTest::test8() +void CV_RotatedRectangleIntersectionTest::test9() { // full intersection, rectangle fully enclosed in the other + RotatedRect rect1(Point2f(0, 0), Size2f(2, 2), 0.0f); + RotatedRect rect2(Point2f(2, 0), Size2f(2, 123.45f), 0.0f); - RotatedRect rect1, rect2; + vector vertices; + int ret = rotatedRectangleIntersection(rect1, rect2, vertices); + + CV_Assert(ret == INTERSECT_PARTIAL); - rect1.center.x = 0; - rect1.center.y = 0; - rect1.size.width = 2; - rect1.size.height = 2; - rect1.angle = 0; + vector targetVertices(2); + targetVertices[0] = Point2f(1.0f, -1.0f); + targetVertices[1] = Point2f(1.0f, 1.0f); + compare(vertices, targetVertices); +} - rect2.center.x = 2; - rect2.center.y = 2; - rect2.size.width = 2; - rect2.size.height = 2; - rect2.angle = 0; +void CV_RotatedRectangleIntersectionTest::test10() +{ + // three points of rect2 are inside rect1. + RotatedRect rect1(Point2f(0, 0), Size2f(2, 2), 0.0f); + RotatedRect rect2(Point2f(0, 0.5), Size2f(1, 1), 45.0f); vector vertices; - int ret = rotatedRectangleIntersection(rect1, rect2, vertices); CV_Assert(ret == INTERSECT_PARTIAL); - CV_Assert(vertices.size() == 1); - - double dx = vertices[0].x - 1; - double dy = vertices[0].y - 1; - double r = sqrt(dx*dx + dy*dy); - CV_Assert(r < ACCURACY); + vector targetVertices(5); + targetVertices[0] = Point2f(0.207107f, 1.0f); + targetVertices[1] = Point2f(-0.207107f, 1.0f); + targetVertices[2] = Point2f(-0.707107f, 0.5f); + targetVertices[3] = Point2f(0.0f, -0.207107f); + targetVertices[4] = Point2f(0.707107f, 0.5f); + compare(vertices, targetVertices); } -void CV_RotatedRectangleIntersectionTest::test9() +void CV_RotatedRectangleIntersectionTest::test11() { - // full intersection, rectangle fully enclosed in the other + RotatedRect rect1(Point2f(0, 0), Size2f(4, 2), 0.0f); + RotatedRect rect2(Point2f(0, 0), Size2f(2, 2), -45.0f); - RotatedRect rect1, rect2; + vector vertices; + int ret = rotatedRectangleIntersection(rect1, rect2, vertices); - rect1.center.x = 0; - rect1.center.y = 0; - rect1.size.width = 2; - rect1.size.height = 2; - rect1.angle = 0; + CV_Assert(ret == INTERSECT_PARTIAL); - rect2.center.x = 2; - rect2.center.y = 0; - rect2.size.width = 2; - rect2.size.height = 123.45f; - rect2.angle = 0; + vector targetVertices(6); + targetVertices[0] = Point2f(-0.414214f, -1.0f); + targetVertices[1] = Point2f(0.414213f, -1.0f); + targetVertices[2] = Point2f(1.41421f, 0.0f); + targetVertices[3] = Point2f(0.414214f, 1.0f); + targetVertices[4] = Point2f(-0.414213f, 1.0f); + targetVertices[5] = Point2f(-1.41421f, 0.0f); + compare(vertices, targetVertices); +} - vector vertices; +void CV_RotatedRectangleIntersectionTest::test12() +{ + RotatedRect rect1(Point2f(0, 0), Size2f(2, 2), 0.0f); + RotatedRect rect2(Point2f(0, 1), Size2f(1, 1), 0.0f); + vector vertices; int ret = rotatedRectangleIntersection(rect1, rect2, vertices); CV_Assert(ret == INTERSECT_PARTIAL); - CV_Assert(vertices.size() == 2); - vector possibleVertices(2); + vector targetVertices(4); + targetVertices[0] = Point2f(-0.5f, 1.0f); + targetVertices[1] = Point2f(-0.5f, 0.5f); + targetVertices[2] = Point2f(0.5f, 0.5f); + targetVertices[3] = Point2f(0.5f, 1.0f); + compare(vertices, targetVertices); +} - possibleVertices[0] = Point2f(1.0f, 1.0f); - possibleVertices[1] = Point2f(1.0f, -1.0f); +void CV_RotatedRectangleIntersectionTest::test13() +{ + RotatedRect rect1(Point2f(0, 0), Size2f(1, 3), 0.0f); + RotatedRect rect2(Point2f(0, 1), Size2f(3, 1), 0.0f); - for( size_t i = 0; i < vertices.size(); i++ ) - { - double bestR = DBL_MAX; + vector vertices; + int ret = rotatedRectangleIntersection(rect1, rect2, vertices); - for( size_t j = 0; j < possibleVertices.size(); j++ ) - { - double dx = vertices[i].x - possibleVertices[j].x; - double dy = vertices[i].y - possibleVertices[j].y; - double r = sqrt(dx*dx + dy*dy); + CV_Assert(ret == INTERSECT_PARTIAL); - bestR = std::min(bestR, r); - } + vector targetVertices(4); + targetVertices[0] = Point2f(-0.5f, 0.5f); + targetVertices[1] = Point2f(0.5f, 0.5f); + targetVertices[2] = Point2f(0.5f, 1.5f); + targetVertices[3] = Point2f(-0.5f, 1.5f); + compare(vertices, targetVertices); +} - CV_Assert(bestR < ACCURACY); +void CV_RotatedRectangleIntersectionTest::test14() +{ + const int kNumTests = 100; + const int kWidth = 5; + const int kHeight = 5; + RotatedRect rects[2]; + std::vector inter; + for (int i = 0; i < kNumTests; ++i) + { + for (int j = 0; j < 2; ++j) + { + rects[j].center = Point2f((float)(rand() % kWidth), (float)(rand() % kHeight)); + rects[j].size = Size2f(rand() % kWidth + 1.0f, rand() % kHeight + 1.0f); + rects[j].angle = (float)(rand() % 360); + } + rotatedRectangleIntersection(rects[0], rects[1], inter); + ASSERT_TRUE(inter.size() < 4 || isContourConvex(inter)); } } diff --git a/samples/dnn/text_detection.cpp b/samples/dnn/text_detection.cpp index 48157d8a13..5abe6b6884 100644 --- a/samples/dnn/text_detection.cpp +++ b/samples/dnn/text_detection.cpp @@ -124,17 +124,14 @@ void decode(const Mat& scores, const Mat& geometry, float scoreThresh, const int height = scores.size[2]; const int width = scores.size[3]; - const int planeSize = height * width; - - float* scoresData = (float*)scores.data; - float* geometryData = (float*)geometry.data; - float* x0_data = geometryData; - float* x1_data = geometryData + planeSize; - float* x2_data = geometryData + planeSize * 2; - float* x3_data = geometryData + planeSize * 3; - float* anglesData = geometryData + planeSize * 4; for (int y = 0; y < height; ++y) { + const float* scoresData = scores.ptr(0, 0, y); + const float* x0_data = geometry.ptr(0, 0, y); + const float* x1_data = geometry.ptr(0, 1, y); + const float* x2_data = geometry.ptr(0, 2, y); + const float* x3_data = geometry.ptr(0, 3, y); + const float* anglesData = geometry.ptr(0, 4, y); for (int x = 0; x < width; ++x) { float score = scoresData[x]; @@ -142,7 +139,6 @@ void decode(const Mat& scores, const Mat& geometry, float scoreThresh, continue; // Decode a prediction. - // Multiple by 4 because feature maps are 4 time less than input image. float offsetX = x * 4.0f, offsetY = y * 4.0f; float angle = anglesData[x]; @@ -159,11 +155,5 @@ void decode(const Mat& scores, const Mat& geometry, float scoreThresh, detections.push_back(r); confidences.push_back(score); } - scoresData += width; - x0_data += width; - x1_data += width; - x2_data += width; - x3_data += width; - anglesData += width; } }