| #include "DataTypes.h" |
| |
| // Sources |
| // computer-aided design - volume 22 number 9 november 1990 pp 538 - 549 |
| // online at http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf |
| |
| // This turns a line segment into a parameterized line, of the form |
| // ax + by + c = 0 |
| // When a^2 + b^2 == 1, the line is normalized. |
| // The distance to the line for (x, y) is d(x,y) = ax + by + c |
| // |
| // Note that the distances below are not necessarily normalized. To get the true |
| // distance, it's necessary to either call normalize() after xxxEndPoints(), or |
| // divide the result of xxxDistance() by sqrt(normalSquared()) |
| |
| class LineParameters { |
| public: |
| void cubicEndPoints(const Cubic& pts) { |
| a = pts[0].y - pts[3].y; |
| b = pts[3].x - pts[0].x; |
| c = pts[0].x * pts[3].y - pts[3].x * pts[0].y; |
| } |
| |
| void cubicEndPoints(const Cubic& pts, int s, int e) { |
| a = pts[s].y - pts[e].y; |
| b = pts[e].x - pts[s].x; |
| c = pts[s].x * pts[e].y - pts[e].x * pts[s].y; |
| } |
| |
| void lineEndPoints(const _Line& pts) { |
| a = pts[0].y - pts[1].y; |
| b = pts[1].x - pts[0].x; |
| c = pts[0].x * pts[1].y - pts[1].x * pts[0].y; |
| } |
| |
| void quadEndPoints(const Quadratic& pts) { |
| a = pts[0].y - pts[2].y; |
| b = pts[2].x - pts[0].x; |
| c = pts[0].x * pts[2].y - pts[2].x * pts[0].y; |
| } |
| |
| void quadEndPoints(const Quadratic& pts, int s, int e) { |
| a = pts[s].y - pts[e].y; |
| b = pts[e].x - pts[s].x; |
| c = pts[s].x * pts[e].y - pts[e].x * pts[s].y; |
| } |
| |
| double normalSquared() { |
| return a * a + b * b; |
| } |
| |
| bool normalize() { |
| double normal = sqrt(normalSquared()); |
| if (approximately_zero_squared(normal)) { |
| a = b = c = 0; |
| return false; |
| } |
| double reciprocal = 1 / normal; |
| a *= reciprocal; |
| b *= reciprocal; |
| c *= reciprocal; |
| return true; |
| } |
| |
| void cubicDistanceY(const Cubic& pts, Cubic& distance) { |
| double oneThird = 1 / 3.0; |
| for (int index = 0; index < 4; ++index) { |
| distance[index].x = index * oneThird; |
| distance[index].y = a * pts[index].x + b * pts[index].y + c; |
| } |
| } |
| |
| void quadDistanceY(const Quadratic& pts, Quadratic& distance) { |
| double oneHalf = 1 / 2.0; |
| for (int index = 0; index < 3; ++index) { |
| distance[index].x = index * oneHalf; |
| distance[index].y = a * pts[index].x + b * pts[index].y + c; |
| } |
| } |
| |
| void controlPtDistance(const Cubic& pts, double distance[2]) { |
| for (int index = 0; index < 2; ++index) { |
| distance[index] = a * pts[index + 1].x + b * pts[index + 1].y + c; |
| } |
| } |
| |
| void controlPtDistance(const Cubic& pts, int i, int j, double distance[2]) { |
| distance[0] = a * pts[i].x + b * pts[i].y + c; |
| distance[1] = a * pts[j].x + b * pts[j].y + c; |
| } |
| |
| double controlPtDistance(const Quadratic& pts) { |
| return a * pts[1].x + b * pts[1].y + c; |
| } |
| |
| double pointDistance(const _Point& pt) { |
| return a * pt.x + b * pt.y + c; |
| } |
| |
| private: |
| double a; |
| double b; |
| double c; |
| }; |