Module org.jhotdraw8.geom

Package org.jhotdraw8.geom.intersect

Class IntersectCubicCurvePoint

java.lang.Object

org.jhotdraw8.geom.intersect.IntersectCubicCurvePoint

public class IntersectCubicCurvePoint
extends Object

Method Summary

Modifier and Type	Method	Description
static @NonNull IntersectionResult	intersectCubicCurvePoint(double x0, double y0, double x1, double y1, double x2, double y2, double x3, double y3, double cx, double cy, double epsilon)	Computes the intersection between a quadratic bezier curve and a point with a tolerance radius.
static @NonNull IntersectionResultEx	intersectCubicCurvePointEx(double x0, double y0, double x1, double y1, double x2, double y2, double x3, double y3, double cx, double cy)
static @NonNull IntersectionResultEx	intersectCubicCurvePointEx(double a0x, double a0y, double a1x, double a1y, double a2x, double a2y, double a3x, double a3y, double cx, double cy, double epsilon)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

intersectCubicCurvePointEx

public static @NonNull IntersectionResultEx intersectCubicCurvePointEx(double x0,
 double y0,
 double x1,
 double y1,
 double x2,
 double y2,
 double x3,
 double y3,
 double cx,
 double cy)

intersectCubicCurvePointEx

public static @NonNull IntersectionResultEx intersectCubicCurvePointEx(double a0x,
 double a0y,
 double a1x,
 double a1y,
 double a2x,
 double a2y,
 double a3x,
 double a3y,
 double cx,
 double cy,
 double epsilon)

intersectCubicCurvePoint

public static @NonNull IntersectionResult intersectCubicCurvePoint(double x0,
 double y0,
 double x1,
 double y1,
 double x2,
 double y2,
 double x3,
 double y3,
 double cx,
 double cy,
 double epsilon)

Computes the intersection between a quadratic bezier curve and a point with a tolerance radius.

This method solves the last equation shown in the list below.

1. (1 - t)³·p0 + 3·(1 - t)²·t·p1 + 3·(1 - t)·t²·p2 + t³·p3 , 0 ≤ t ≤ 1
   : cubic bezier equation, vector form
2. -(p0 - 3*p1 + 3*p2 - p3)*t^3 + 3*(p0 - 2*p1 + p2)*t^2 - 3*(p0 - p1)*t + p0
   : expanded, and then collected for t
3. c3·t³ + c2·t² + c1·t + c0
   : coefficients compacted
4. c3x·t³ + c2x·t² + c1x·t + c0x , c3y·t³ + c2y·t² + c1y·t + c0y
   : bezier equation in matrix form
5. fx , fy
   : compacted matrix form
6. (fx - cx)² + (fy - cy)² = 0
   : distance to point equation, with fx, fy inserted from matrix form
7. c3x^2*t^6 + 2*c2x*c3x*t^5 + (c2x^2 + 2*c1x*c3x)*t^4 + 2*(c1x*c2x + c0x*c3x - c3x*cx)*t^3 + (c1x^2 + 2*c0x*c2x - 2*c2x*cx)*t^2 + c0x^2 - 2*c0x*cx + cx^2 + 2*(c0x*c1x - c1x*cx)*t
   + ..same for y-axis...
   : coefficients expanded
8. (c3x^2 + c3y^2)*t^6
   + 2*(c2x*c3x + c2y*c3y)*t^5
   + (c2x^2 + c2y^2 + 2*c1x*c3x + 2*c1y*c3y)*t^4
   + 2*(c1x*c2x + c1y*c2y + c0x*c3x + c0y*c3y - c3x*cx - c3y*cy)*t^3
   + (c1x^2 + c1y^2 + 2*c0x*c2x + 2*c0y*c2y - 2*c2x*cx - 2*c2y*cy)*t^2
   + 2*(c0x*c1x + c0y*c1y - c1x*cx - c1y*cy)*t
   + c0x^2 + c0y^2 - 2*c0x*cx + cx^2 - 2*c0y*cy + cy^2
   : coefficients collected for t
9. a·t⁶ + b·t⁵ + c·t⁴ + d·t³ + e·t² + f·t + g = 0, 0 ≤ t ≤ 1
   : final polynomial equation
10. 6·a·t⁵ + 5·b·t⁴ + 4·c·t³ + 3·d·t² + 2·e·t + f = 0, 0 ≤ t ≤ 1
    : derivative

Parameters:

x0 - x-coordinate of control point P0 of the bezier curve

y0 - y-coordinate of control point P0 of the bezier curve

x1 - x-coordinate of control point P1 of the bezier curve

y1 - y-coordinate of control point P1 of the bezier curve

x2 - x-coordinate of control point P2 of the bezier curve

y2 - y-coordinate of control point P2 of the bezier curve

x3 - x-coordinate of control point P3 of the bezier curve

y3 - y-coordinate of control point P3 of the bezier curve

cx - x-coordinate of the point

cy - y-coordinate of the point

epsilon - the tolerance radius

Returns:

the intersection