com.sun.javafx.geom.CubicCurve2D Maven / Gradle / Ivy
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package com.sun.javafx.geom;
import java.util.Arrays;
import com.sun.javafx.geom.transform.BaseTransform;
/**
* The CubicCurve2D class defines a cubic parametric curve
* segment in {@code (x,y)} coordinate space.
*
* This class is only the abstract superclass for all objects which
* store a 2D cubic curve segment.
* The actual storage representation of the coordinates is left to
* the subclass.
*
* @version 1.42, 05/05/07
*/
public class CubicCurve2D extends Shape {
/**
* The X coordinate of the start point
* of the cubic curve segment.
*/
public float x1;
/**
* The Y coordinate of the start point
* of the cubic curve segment.
*/
public float y1;
/**
* The X coordinate of the first control point
* of the cubic curve segment.
*/
public float ctrlx1;
/**
* The Y coordinate of the first control point
* of the cubic curve segment.
*/
public float ctrly1;
/**
* The X coordinate of the second control point
* of the cubic curve segment.
*/
public float ctrlx2;
/**
* The Y coordinate of the second control point
* of the cubic curve segment.
*/
public float ctrly2;
/**
* The X coordinate of the end point
* of the cubic curve segment.
*/
public float x2;
/**
* The Y coordinate of the end point
* of the cubic curve segment.
*/
public float y2;
/**
* Constructs and initializes a CubicCurve with coordinates
* (0, 0, 0, 0, 0, 0, 0, 0).
*/
public CubicCurve2D() { }
/**
* Constructs and initializes a {@code CubicCurve2D} from
* the specified {@code float} coordinates.
*
* @param x1 the X coordinate for the start point
* of the resulting {@code CubicCurve2D}
* @param y1 the Y coordinate for the start point
* of the resulting {@code CubicCurve2D}
* @param ctrlx1 the X coordinate for the first control point
* of the resulting {@code CubicCurve2D}
* @param ctrly1 the Y coordinate for the first control point
* of the resulting {@code CubicCurve2D}
* @param ctrlx2 the X coordinate for the second control point
* of the resulting {@code CubicCurve2D}
* @param ctrly2 the Y coordinate for the second control point
* of the resulting {@code CubicCurve2D}
* @param x2 the X coordinate for the end point
* of the resulting {@code CubicCurve2D}
* @param y2 the Y coordinate for the end point
* of the resulting {@code CubicCurve2D}
*/
public CubicCurve2D(float x1, float y1,
float ctrlx1, float ctrly1,
float ctrlx2, float ctrly2,
float x2, float y2)
{
setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2);
}
/**
* Sets the location of the end points and control points
* of this curve to the specified {@code float} coordinates.
*
* @param x1 the X coordinate used to set the start point
* of this {@code CubicCurve2D}
* @param y1 the Y coordinate used to set the start point
* of this {@code CubicCurve2D}
* @param ctrlx1 the X coordinate used to set the first control point
* of this {@code CubicCurve2D}
* @param ctrly1 the Y coordinate used to set the first control point
* of this {@code CubicCurve2D}
* @param ctrlx2 the X coordinate used to set the second control point
* of this {@code CubicCurve2D}
* @param ctrly2 the Y coordinate used to set the second control point
* of this {@code CubicCurve2D}
* @param x2 the X coordinate used to set the end point
* of this {@code CubicCurve2D}
* @param y2 the Y coordinate used to set the end point
* of this {@code CubicCurve2D}
*/
public void setCurve(float x1, float y1,
float ctrlx1, float ctrly1,
float ctrlx2, float ctrly2,
float x2, float y2)
{
this.x1 = x1;
this.y1 = y1;
this.ctrlx1 = ctrlx1;
this.ctrly1 = ctrly1;
this.ctrlx2 = ctrlx2;
this.ctrly2 = ctrly2;
this.x2 = x2;
this.y2 = y2;
}
/**
* {@inheritDoc}
*/
@Override
public RectBounds getBounds() {
float left = Math.min(Math.min(x1, x2),
Math.min(ctrlx1, ctrlx2));
float top = Math.min(Math.min(y1, y2),
Math.min(ctrly1, ctrly2));
float right = Math.max(Math.max(x1, x2),
Math.max(ctrlx1, ctrlx2));
float bottom = Math.max(Math.max(y1, y2),
Math.max(ctrly1, ctrly2));
return new RectBounds(left, top, right, bottom);
}
/**
* Evaluates this cubic curve at the given parameter value, where
* it is expected, but not required, that the parameter will be
* between 0 and 1. 0 corresponds to the start point of the curve
* and 1 corresponds to the end point of the curve.
* @param t parameter value at which to evaluate the curve
* @return a newly allocated Point2D containing the evaluation of
* the curve at that parameter value
*/
public Point2D eval(float t) {
Point2D result = new Point2D();
eval(t, result);
return result;
}
/**
* Evaluates this cubic curve at the given parameter value, where
* it is expected, but not required, that the parameter will be
* between 0 and 1. 0 corresponds to the start point of the curve
* and 1 corresponds to the end point of the curve.
* @param td parameter value at which to evaluate the curve
* @param result Point2D in to which to store the evaluation of
* the curve at that parameter value
*/
public void eval(float td, Point2D result) {
result.setLocation(calcX(td), calcY(td));
}
/**
* Evaluates the derivative of this cubic curve at the given
* parameter value, where it is expected, but not required, that
* the parameter will be between 0 and 1. 0 corresponds to the
* derivative at the start point of the curve and 1 corresponds to
* the derivative at the end point of the curve.
* @param t parameter value at which to compute the derivative of
* the curve
* @return a newly allocated Point2D containing the derivative of
* the curve at that parameter value
*/
public Point2D evalDt(float t) {
Point2D result = new Point2D();
evalDt(t, result);
return result;
}
/**
* Evaluates the derivative of this cubic curve at the given
* parameter value, where it is expected, but not required, that
* the parameter will be between 0 and 1. 0 corresponds to the
* derivative at the start point of the curve and 1 corresponds to
* the derivative at the end point of the curve.
* @param t parameter value at which to compute the derivative of
* the curve
* @param result Point2D in to which to store the derivative of
* the curve at that parameter value
*/
public void evalDt(float td, Point2D result) {
float t = td;
float u = 1 - t;
float x = 3*((ctrlx1-x1)*u*u +
2*(ctrlx2-ctrlx1)*u*t +
(x2-ctrlx2)*t*t);
float y = 3*((ctrly1-y1)*u*u +
2*(ctrly2-ctrly1)*u*t +
(y2-ctrly2)*t*t);
result.setLocation(x, y);
}
/**
* Sets the location of the end points and control points of this curve
* to the double coordinates at the specified offset in the specified
* array.
* @param coords a double array containing coordinates
* @param offset the index of coords from which to begin
* setting the end points and control points of this curve
* to the coordinates contained in coords
*/
public void setCurve(float[] coords, int offset) {
setCurve(coords[offset + 0], coords[offset + 1],
coords[offset + 2], coords[offset + 3],
coords[offset + 4], coords[offset + 5],
coords[offset + 6], coords[offset + 7]);
}
/**
* Sets the location of the end points and control points of this curve
* to the specified Point2D coordinates.
* @param p1 the first specified Point2D used to set the
* start point of this curve
* @param cp1 the second specified Point2D used to set the
* first control point of this curve
* @param cp2 the third specified Point2D used to set the
* second control point of this curve
* @param p2 the fourth specified Point2D used to set the
* end point of this curve
*/
public void setCurve(Point2D p1, Point2D cp1, Point2D cp2, Point2D p2) {
setCurve(p1.x, p1.y, cp1.x, cp1.y, cp2.x, cp2.y, p2.x, p2.y);
}
/**
* Sets the location of the end points and control points of this curve
* to the coordinates of the Point2D objects at the specified
* offset in the specified array.
* @param pts an array of Point2D objects
* @param offset the index of pts from which to begin setting
* the end points and control points of this curve to the
* points contained in pts
*/
public void setCurve(Point2D[] pts, int offset) {
setCurve(pts[offset + 0].x, pts[offset + 0].y,
pts[offset + 1].x, pts[offset + 1].y,
pts[offset + 2].x, pts[offset + 2].y,
pts[offset + 3].x, pts[offset + 3].y);
}
/**
* Sets the location of the end points and control points of this curve
* to the same as those in the specified CubicCurve2D.
* @param c the specified CubicCurve2D
*/
public void setCurve(CubicCurve2D c) {
setCurve(c.x1, c.y1, c.ctrlx1, c.ctrly1, c.ctrlx2, c.ctrly2, c.x2, c.y2);
}
/**
* Returns the square of the flatness of the cubic curve specified
* by the indicated control points. The flatness is the maximum distance
* of a control point from the line connecting the end points.
*
* @param x1 the X coordinate that specifies the start point
* of a {@code CubicCurve2D}
* @param y1 the Y coordinate that specifies the start point
* of a {@code CubicCurve2D}
* @param ctrlx1 the X coordinate that specifies the first control point
* of a {@code CubicCurve2D}
* @param ctrly1 the Y coordinate that specifies the first control point
* of a {@code CubicCurve2D}
* @param ctrlx2 the X coordinate that specifies the second control point
* of a {@code CubicCurve2D}
* @param ctrly2 the Y coordinate that specifies the second control point
* of a {@code CubicCurve2D}
* @param x2 the X coordinate that specifies the end point
* of a {@code CubicCurve2D}
* @param y2 the Y coordinate that specifies the end point
* of a {@code CubicCurve2D}
* @return the square of the flatness of the {@code CubicCurve2D}
* represented by the specified coordinates.
*/
public static float getFlatnessSq(float x1, float y1,
float ctrlx1, float ctrly1,
float ctrlx2, float ctrly2,
float x2, float y2) {
return Math.max(Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx1, ctrly1),
Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx2, ctrly2));
}
/**
* Returns the flatness of the cubic curve specified
* by the indicated control points. The flatness is the maximum distance
* of a control point from the line connecting the end points.
*
* @param x1 the X coordinate that specifies the start point
* of a {@code CubicCurve2D}
* @param y1 the Y coordinate that specifies the start point
* of a {@code CubicCurve2D}
* @param ctrlx1 the X coordinate that specifies the first control point
* of a {@code CubicCurve2D}
* @param ctrly1 the Y coordinate that specifies the first control point
* of a {@code CubicCurve2D}
* @param ctrlx2 the X coordinate that specifies the second control point
* of a {@code CubicCurve2D}
* @param ctrly2 the Y coordinate that specifies the second control point
* of a {@code CubicCurve2D}
* @param x2 the X coordinate that specifies the end point
* of a {@code CubicCurve2D}
* @param y2 the Y coordinate that specifies the end point
* of a {@code CubicCurve2D}
* @return the flatness of the {@code CubicCurve2D}
* represented by the specified coordinates.
*/
public static float getFlatness(float x1, float y1,
float ctrlx1, float ctrly1,
float ctrlx2, float ctrly2,
float x2, float y2) {
return (float) Math.sqrt(getFlatnessSq(x1, y1, ctrlx1, ctrly1,
ctrlx2, ctrly2, x2, y2));
}
/**
* Returns the square of the flatness of the cubic curve specified
* by the control points stored in the indicated array at the
* indicated index. The flatness is the maximum distance
* of a control point from the line connecting the end points.
* @param coords an array containing coordinates
* @param offset the index of coords from which to begin
* getting the end points and control points of the curve
* @return the square of the flatness of the CubicCurve2D
* specified by the coordinates in coords at
* the specified offset.
*/
public static float getFlatnessSq(float coords[], int offset) {
return getFlatnessSq(coords[offset + 0], coords[offset + 1],
coords[offset + 2], coords[offset + 3],
coords[offset + 4], coords[offset + 5],
coords[offset + 6], coords[offset + 7]);
}
/**
* Returns the flatness of the cubic curve specified
* by the control points stored in the indicated array at the
* indicated index. The flatness is the maximum distance
* of a control point from the line connecting the end points.
* @param coords an array containing coordinates
* @param offset the index of coords from which to begin
* getting the end points and control points of the curve
* @return the flatness of the CubicCurve2D
* specified by the coordinates in coords at
* the specified offset.
*/
public static float getFlatness(float coords[], int offset) {
return getFlatness(coords[offset + 0], coords[offset + 1],
coords[offset + 2], coords[offset + 3],
coords[offset + 4], coords[offset + 5],
coords[offset + 6], coords[offset + 7]);
}
/**
* Returns the square of the flatness of this curve. The flatness is the
* maximum distance of a control point from the line connecting the
* end points.
* @return the square of the flatness of this curve.
*/
public float getFlatnessSq() {
return getFlatnessSq(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2);
}
/**
* Returns the flatness of this curve. The flatness is the
* maximum distance of a control point from the line connecting the
* end points.
* @return the flatness of this curve.
*/
public float getFlatness() {
return getFlatness(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2);
}
/**
* Subdivides this cubic curve at the given parameter value
* (expected to be between 0 and 1) and stores the resulting two
* subdivided curves into the left and right curve parameters.
* Either or both of the left and right objects may be the same as
* this object or null.
* @param t the parameter value at which to subdivide the curve
* @param left the cubic curve object for storing for the left or
* first portion of the subdivided curve
* @param right the cubic curve object for storing for the right or
* second portion of the subdivided curve
*/
public void subdivide(float t, CubicCurve2D left, CubicCurve2D right) {
if ((left == null) && (right == null)) return;
float npx = calcX(t);
float npy = calcY(t);
float x1 = this.x1;
float y1 = this.y1;
float c1x = this.ctrlx1;
float c1y = this.ctrly1;
float c2x = this.ctrlx2;
float c2y = this.ctrly2;
float x2 = this.x2;
float y2 = this.y2;
float u = 1-t;
float hx = u*c1x+t*c2x;
float hy = u*c1y+t*c2y;
if (left != null) {
float lx1 = x1;
float ly1 = y1;
float lc1x = u*x1+t*c1x;
float lc1y = u*y1+t*c1y;
float lc2x = u*lc1x+t*hx;
float lc2y = u*lc1y+t*hy;
float lx2 = npx;
float ly2 = npy;
left.setCurve(lx1, ly1,
lc1x, lc1y,
lc2x, lc2y,
lx2, ly2);
}
if (right != null) {
float rx1 = npx;
float ry1 = npy;
float rc2x = u*c2x+t*x2;
float rc2y = u*c2y+t*y2;
float rc1x = u*hx+t*rc2x;
float rc1y = u*hy+t*rc2y;
float rx2 = x2;
float ry2 = y2;
right.setCurve(rx1, ry1,
rc1x, rc1y,
rc2x, rc2y,
rx2, ry2);
}
}
/**
* Subdivides this cubic curve and stores the resulting two
* subdivided curves into the left and right curve parameters.
* Either or both of the left and right objects may be the same
* as this object or null.
* @param left the cubic curve object for storing for the left or
* first half of the subdivided curve
* @param right the cubic curve object for storing for the right or
* second half of the subdivided curve
*/
public void subdivide(CubicCurve2D left, CubicCurve2D right) {
subdivide(this, left, right);
}
/**
* Subdivides the cubic curve specified by the src parameter
* and stores the resulting two subdivided curves into the
* left and right curve parameters.
* Either or both of the left and right objects
* may be the same as the src object or null.
* @param src the cubic curve to be subdivided
* @param left the cubic curve object for storing the left or
* first half of the subdivided curve
* @param right the cubic curve object for storing the right or
* second half of the subdivided curve
*/
public static void subdivide(CubicCurve2D src,
CubicCurve2D left,
CubicCurve2D right) {
float x1 = src.x1;
float y1 = src.y1;
float ctrlx1 = src.ctrlx1;
float ctrly1 = src.ctrly1;
float ctrlx2 = src.ctrlx2;
float ctrly2 = src.ctrly2;
float x2 = src.x2;
float y2 = src.y2;
float centerx = (ctrlx1 + ctrlx2) / 2f;
float centery = (ctrly1 + ctrly2) / 2f;
ctrlx1 = (x1 + ctrlx1) / 2f;
ctrly1 = (y1 + ctrly1) / 2f;
ctrlx2 = (x2 + ctrlx2) / 2f;
ctrly2 = (y2 + ctrly2) / 2f;
float ctrlx12 = (ctrlx1 + centerx) / 2f;
float ctrly12 = (ctrly1 + centery) / 2f;
float ctrlx21 = (ctrlx2 + centerx) / 2f;
float ctrly21 = (ctrly2 + centery) / 2f;
centerx = (ctrlx12 + ctrlx21) / 2f;
centery = (ctrly12 + ctrly21) / 2f;
if (left != null) {
left.setCurve(x1, y1, ctrlx1, ctrly1,
ctrlx12, ctrly12, centerx, centery);
}
if (right != null) {
right.setCurve(centerx, centery, ctrlx21, ctrly21,
ctrlx2, ctrly2, x2, y2);
}
}
/**
* Subdivides the cubic curve specified by the coordinates
* stored in the src array at indices srcoff
* through (srcoff + 7) and stores the
* resulting two subdivided curves into the two result arrays at the
* corresponding indices.
* Either or both of the left and right
* arrays may be null or a reference to the same array
* as the src array.
* Note that the last point in the first subdivided curve is the
* same as the first point in the second subdivided curve. Thus,
* it is possible to pass the same array for left
* and right and to use offsets, such as rightoff
* equals (leftoff + 6), in order
* to avoid allocating extra storage for this common point.
* @param src the array holding the coordinates for the source curve
* @param srcoff the offset into the array of the beginning of the
* the 6 source coordinates
* @param left the array for storing the coordinates for the first
* half of the subdivided curve
* @param leftoff the offset into the array of the beginning of the
* the 6 left coordinates
* @param right the array for storing the coordinates for the second
* half of the subdivided curve
* @param rightoff the offset into the array of the beginning of the
* the 6 right coordinates
*/
public static void subdivide(float src[], int srcoff,
float left[], int leftoff,
float right[], int rightoff) {
float x1 = src[srcoff + 0];
float y1 = src[srcoff + 1];
float ctrlx1 = src[srcoff + 2];
float ctrly1 = src[srcoff + 3];
float ctrlx2 = src[srcoff + 4];
float ctrly2 = src[srcoff + 5];
float x2 = src[srcoff + 6];
float y2 = src[srcoff + 7];
if (left != null) {
left[leftoff + 0] = x1;
left[leftoff + 1] = y1;
}
if (right != null) {
right[rightoff + 6] = x2;
right[rightoff + 7] = y2;
}
x1 = (x1 + ctrlx1) / 2f;
y1 = (y1 + ctrly1) / 2f;
x2 = (x2 + ctrlx2) / 2f;
y2 = (y2 + ctrly2) / 2f;
float centerx = (ctrlx1 + ctrlx2) / 2f;
float centery = (ctrly1 + ctrly2) / 2f;
ctrlx1 = (x1 + centerx) / 2f;
ctrly1 = (y1 + centery) / 2f;
ctrlx2 = (x2 + centerx) / 2f;
ctrly2 = (y2 + centery) / 2f;
centerx = (ctrlx1 + ctrlx2) / 2f;
centery = (ctrly1 + ctrly2) / 2f;
if (left != null) {
left[leftoff + 2] = x1;
left[leftoff + 3] = y1;
left[leftoff + 4] = ctrlx1;
left[leftoff + 5] = ctrly1;
left[leftoff + 6] = centerx;
left[leftoff + 7] = centery;
}
if (right != null) {
right[rightoff + 0] = centerx;
right[rightoff + 1] = centery;
right[rightoff + 2] = ctrlx2;
right[rightoff + 3] = ctrly2;
right[rightoff + 4] = x2;
right[rightoff + 5] = y2;
}
}
/**
* Solves the cubic whose coefficients are in the eqn
* array and places the non-complex roots back into the same array,
* returning the number of roots. The solved cubic is represented
* by the equation:
*
* eqn = {c, b, a, d}
* dx^3 + ax^2 + bx + c = 0
*
* A return value of -1 is used to distinguish a constant equation
* that might be always 0 or never 0 from an equation that has no
* zeroes.
* @param eqn an array containing coefficients for a cubic
* @return the number of roots, or -1 if the equation is a constant.
*/
public static int solveCubic(float eqn[]) {
return solveCubic(eqn, eqn);
}
/**
* Solve the cubic whose coefficients are in the eqn
* array and place the non-complex roots into the res
* array, returning the number of roots.
* The cubic solved is represented by the equation:
* eqn = {c, b, a, d}
* dx^3 + ax^2 + bx + c = 0
* A return value of -1 is used to distinguish a constant equation,
* which may be always 0 or never 0, from an equation which has no
* zeroes.
* @param eqn the specified array of coefficients to use to solve
* the cubic equation
* @param res the array that contains the non-complex roots
* resulting from the solution of the cubic equation
* @return the number of roots, or -1 if the equation is a constant
*/
public static int solveCubic(float eqn[], float res[]) {
// From Numerical Recipes, 5.6, Quadratic and Cubic Equations
float d = eqn[3];
if (d == 0f) {
// The cubic has degenerated to quadratic (or line or ...).
return QuadCurve2D.solveQuadratic(eqn, res);
}
float a = eqn[2] / d;
float b = eqn[1] / d;
float c = eqn[0] / d;
int roots = 0;
float Q = (a * a - 3f * b) / 9f;
float R = (2f * a * a * a - 9f * a * b + 27f * c) / 54f;
float R2 = R * R;
float Q3 = Q * Q * Q;
a = a / 3f;
if (R2 < Q3) {
float theta = (float) Math.acos(R / Math.sqrt(Q3));
Q = (float) (-2f * Math.sqrt(Q));
if (res == eqn) {
// Copy the eqn so that we don't clobber it with the
// roots. This is needed so that fixRoots can do its
// work with the original equation.
eqn = new float[4];
System.arraycopy(res, 0, eqn, 0, 4);
}
res[roots++] = (float) (Q * Math.cos(theta / 3f) - a);
res[roots++] = (float) (Q * Math.cos((theta + Math.PI * 2f)/ 3f) - a);
res[roots++] = (float) (Q * Math.cos((theta - Math.PI * 2f)/ 3f) - a);
fixRoots(res, eqn);
} else {
boolean neg = (R < 0f);
float S = (float) Math.sqrt(R2 - Q3);
if (neg) {
R = -R;
}
float A = (float) Math.pow(R + S, 1f / 3f);
if (!neg) {
A = -A;
}
float B = (A == 0f) ? 0f : (Q / A);
res[roots++] = (A + B) - a;
}
return roots;
}
/*
* This pruning step is necessary since solveCubic uses the
* cosine function to calculate the roots when there are 3
* of them. Since the cosine method can have an error of
* +/- 1E-14 we need to make sure that we don't make any
* bad decisions due to an error.
*
* If the root is not near one of the endpoints, then we will
* only have a slight inaccuracy in calculating the x intercept
* which will only cause a slightly wrong answer for some
* points very close to the curve. While the results in that
* case are not as accurate as they could be, they are not
* disastrously inaccurate either.
*
* On the other hand, if the error happens near one end of
* the curve, then our processing to reject values outside
* of the t=[0,1] range will fail and the results of that
* failure will be disastrous since for an entire horizontal
* range of test points, we will either overcount or undercount
* the crossings and get a wrong answer for all of them, even
* when they are clearly and obviously inside or outside the
* curve.
*
* To work around this problem, we try a couple of Newton-Raphson
* iterations to see if the true root is closer to the endpoint
* or further away. If it is further away, then we can stop
* since we know we are on the right side of the endpoint. If
* we change direction, then either we are now being dragged away
* from the endpoint in which case the first condition will cause
* us to stop, or we have passed the endpoint and are headed back.
* In the second case, we simply evaluate the slope at the
* endpoint itself and place ourselves on the appropriate side
* of it or on it depending on that result.
*/
private static void fixRoots(float res[], float eqn[]) {
final float EPSILON = (float) 1E-5; // eek, Rich may have botched this
for (int i = 0; i < 3; i++) {
float t = res[i];
if (Math.abs(t) < EPSILON) {
res[i] = findZero(t, 0, eqn);
} else if (Math.abs(t - 1) < EPSILON) {
res[i] = findZero(t, 1, eqn);
}
}
}
private static float solveEqn(float eqn[], int order, float t) {
float v = eqn[order];
while (--order >= 0) {
v = v * t + eqn[order];
}
return v;
}
private static float findZero(float t, float target, float eqn[]) {
float slopeqn[] = {eqn[1], 2*eqn[2], 3*eqn[3]};
float slope;
float origdelta = 0f;
float origt = t;
while (true) {
slope = solveEqn(slopeqn, 2, t);
if (slope == 0f) {
// At a local minima - must return
return t;
}
float y = solveEqn(eqn, 3, t);
if (y == 0f) {
// Found it! - return it
return t;
}
// assert(slope != 0 && y != 0);
float delta = - (y / slope);
// assert(delta != 0);
if (origdelta == 0f) {
origdelta = delta;
}
if (t < target) {
if (delta < 0f) return t;
} else if (t > target) {
if (delta > 0f) return t;
} else { /* t == target */
return (delta > 0f
? (target + java.lang.Float.MIN_VALUE)
: (target - java.lang.Float.MIN_VALUE));
}
float newt = t + delta;
if (t == newt) {
// The deltas are so small that we aren't moving...
return t;
}
if (delta * origdelta < 0) {
// We have reversed our path.
int tag = (origt < t
? getTag(target, origt, t)
: getTag(target, t, origt));
if (tag != INSIDE) {
// Local minima found away from target - return the middle
return (origt + t) / 2;
}
// Local minima somewhere near target - move to target
// and let the slope determine the resulting t.
t = target;
} else {
t = newt;
}
}
}
/**
* {@inheritDoc}
*/
@Override
public boolean contains(float x, float y) {
if (!(x * 0f + y * 0f == 0f)) {
/* Either x or y was infinite or NaN.
* A NaN always produces a negative response to any test
* and Infinity values cannot be "inside" any path so
* they should return false as well.
*/
return false;
}
// We count the "Y" crossings to determine if the point is
// inside the curve bounded by its closing line.
int crossings =
(Shape.pointCrossingsForLine(x, y, x1, y1, x2, y2) +
Shape.pointCrossingsForCubic(x, y,
x1, y1,
ctrlx1, ctrly1,
ctrlx2, ctrly2,
x2, y2, 0));
return ((crossings & 1) == 1);
}
/**
* {@inheritDoc}
*/
@Override
public boolean contains(Point2D p) {
return contains(p.x, p.y);
}
/*
* Fill an array with the coefficients of the parametric equation
* in t, ready for solving against val with solveCubic.
* We currently have:
*
* val = P(t) = C1(1-t)^3 + 3CP1 t(1-t)^2 + 3CP2 t^2(1-t) + C2 t^3
* = C1 - 3C1t + 3C1t^2 - C1t^3 +
* 3CP1t - 6CP1t^2 + 3CP1t^3 +
* 3CP2t^2 - 3CP2t^3 +
* C2t^3
* 0 = (C1 - val) +
* (3CP1 - 3C1) t +
* (3C1 - 6CP1 + 3CP2) t^2 +
* (C2 - 3CP2 + 3CP1 - C1) t^3
* 0 = C + Bt + At^2 + Dt^3
* C = C1 - val
* B = 3*CP1 - 3*C1
* A = 3*CP2 - 6*CP1 + 3*C1
* D = C2 - 3*CP2 + 3*CP1 - C1
*
*/
private static void fillEqn(float eqn[], float val,
float c1, float cp1, float cp2, float c2) {
eqn[0] = c1 - val;
eqn[1] = (cp1 - c1) * 3f;
eqn[2] = (cp2 - cp1 - cp1 + c1) * 3f;
eqn[3] = c2 + (cp1 - cp2) * 3f - c1;
}
/*
* Evaluate the t values in the first num slots of the vals[] array
* and place the evaluated values back into the same array. Only
* evaluate t values that are within the range <0, 1>, including
* the 0 and 1 ends of the range iff the include0 or include1
* booleans are true. If an "inflection" equation is handed in,
* then any points which represent a point of inflection for that
* cubic equation are also ignored.
*/
private static int evalCubic(float vals[], int num,
boolean include0,
boolean include1,
float inflect[],
float c1, float cp1,
float cp2, float c2) {
int j = 0;
for (int i = 0; i < num; i++) {
float t = vals[i];
if ((include0 ? t >= 0 : t > 0) &&
(include1 ? t <= 1 : t < 1) &&
(inflect == null ||
inflect[1] + (2*inflect[2] + 3*inflect[3]*t)*t != 0))
{
float u = 1 - t;
vals[j++] = c1*u*u*u + 3*cp1*t*u*u + 3*cp2*t*t*u + c2*t*t*t;
}
}
return j;
}
private static final int BELOW = -2;
private static final int LOWEDGE = -1;
private static final int INSIDE = 0;
private static final int HIGHEDGE = 1;
private static final int ABOVE = 2;
/*
* Determine where coord lies with respect to the range from
* low to high. It is assumed that low <= high. The return
* value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE,
* or ABOVE.
*/
private static int getTag(float coord, float low, float high) {
if (coord <= low) {
return (coord < low ? BELOW : LOWEDGE);
}
if (coord >= high) {
return (coord > high ? ABOVE : HIGHEDGE);
}
return INSIDE;
}
/*
* Determine if the pttag represents a coordinate that is already
* in its test range, or is on the border with either of the two
* opttags representing another coordinate that is "towards the
* inside" of that test range. In other words, are either of the
* two "opt" points "drawing the pt inward"?
*/
private static boolean inwards(int pttag, int opt1tag, int opt2tag) {
switch (pttag) {
case BELOW:
case ABOVE:
default:
return false;
case LOWEDGE:
return (opt1tag >= INSIDE || opt2tag >= INSIDE);
case INSIDE:
return true;
case HIGHEDGE:
return (opt1tag <= INSIDE || opt2tag <= INSIDE);
}
}
/**
* {@inheritDoc}
*/
@Override
public boolean intersects(float x, float y, float w, float h) {
// Trivially reject non-existant rectangles
if (w <= 0 || h <= 0) {
return false;
}
// Trivially accept if either endpoint is inside the rectangle
// (not on its border since it may end there and not go inside)
// Record where they lie with respect to the rectangle.
// -1 => left, 0 => inside, 1 => right
float x1 = this.x1;
float y1 = this.y1;
int x1tag = getTag(x1, x, x + w);
int y1tag = getTag(y1, y, y + h);
if (x1tag == INSIDE && y1tag == INSIDE) {
return true;
}
float x2 = this.x2;
float y2 = this.y2;
int x2tag = getTag(x2, x, x + w);
int y2tag = getTag(y2, y, y + h);
if (x2tag == INSIDE && y2tag == INSIDE) {
return true;
}
float ctrlx1 = this.ctrlx1;
float ctrly1 = this.ctrly1;
float ctrlx2 = this.ctrlx2;
float ctrly2 = this.ctrly2;
int ctrlx1tag = getTag(ctrlx1, x, x + w);
int ctrly1tag = getTag(ctrly1, y, y + h);
int ctrlx2tag = getTag(ctrlx2, x, x + w);
int ctrly2tag = getTag(ctrly2, y, y + h);
// Trivially reject if all points are entirely to one side of
// the rectangle.
if (x1tag < INSIDE && x2tag < INSIDE &&
ctrlx1tag < INSIDE && ctrlx2tag < INSIDE)
{
return false; // All points left
}
if (y1tag < INSIDE && y2tag < INSIDE &&
ctrly1tag < INSIDE && ctrly2tag < INSIDE)
{
return false; // All points above
}
if (x1tag > INSIDE && x2tag > INSIDE &&
ctrlx1tag > INSIDE && ctrlx2tag > INSIDE)
{
return false; // All points right
}
if (y1tag > INSIDE && y2tag > INSIDE &&
ctrly1tag > INSIDE && ctrly2tag > INSIDE)
{
return false; // All points below
}
// Test for endpoints on the edge where either the segment
// or the curve is headed "inwards" from them
// Note: These tests are a superset of the fast endpoint tests
// above and thus repeat those tests, but take more time
// and cover more cases
if (inwards(x1tag, x2tag, ctrlx1tag) &&
inwards(y1tag, y2tag, ctrly1tag))
{
// First endpoint on border with either edge moving inside
return true;
}
if (inwards(x2tag, x1tag, ctrlx2tag) &&
inwards(y2tag, y1tag, ctrly2tag))
{
// Second endpoint on border with either edge moving inside
return true;
}
// Trivially accept if endpoints span directly across the rectangle
boolean xoverlap = (x1tag * x2tag <= 0);
boolean yoverlap = (y1tag * y2tag <= 0);
if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) {
return true;
}
if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) {
return true;
}
// We now know that both endpoints are outside the rectangle
// but the 4 points are not all on one side of the rectangle.
// Therefore the curve cannot be contained inside the rectangle,
// but the rectangle might be contained inside the curve, or
// the curve might intersect the boundary of the rectangle.
float[] eqn = new float[4];
float[] res = new float[4];
if (!yoverlap) {
// Both y coordinates for the closing segment are above or
// below the rectangle which means that we can only intersect
// if the curve crosses the top (or bottom) of the rectangle
// in more than one place and if those crossing locations
// span the horizontal range of the rectangle.
fillEqn(eqn, (y1tag < INSIDE ? y : y+h), y1, ctrly1, ctrly2, y2);
int num = solveCubic(eqn, res);
num = evalCubic(res, num, true, true, null,
x1, ctrlx1, ctrlx2, x2);
// odd counts imply the crossing was out of [0,1] bounds
// otherwise there is no way for that part of the curve to
// "return" to meet its endpoint
return (num == 2 &&
getTag(res[0], x, x+w) * getTag(res[1], x, x+w) <= 0);
}
// Y ranges overlap. Now we examine the X ranges
if (!xoverlap) {
// Both x coordinates for the closing segment are left of
// or right of the rectangle which means that we can only
// intersect if the curve crosses the left (or right) edge
// of the rectangle in more than one place and if those
// crossing locations span the vertical range of the rectangle.
fillEqn(eqn, (x1tag < INSIDE ? x : x+w), x1, ctrlx1, ctrlx2, x2);
int num = solveCubic(eqn, res);
num = evalCubic(res, num, true, true, null,
y1, ctrly1, ctrly2, y2);
// odd counts imply the crossing was out of [0,1] bounds
// otherwise there is no way for that part of the curve to
// "return" to meet its endpoint
return (num == 2 &&
getTag(res[0], y, y+h) * getTag(res[1], y, y+h) <= 0);
}
// The X and Y ranges of the endpoints overlap the X and Y
// ranges of the rectangle, now find out how the endpoint
// line segment intersects the Y range of the rectangle
float dx = x2 - x1;
float dy = y2 - y1;
float k = y2 * x1 - x2 * y1;
int c1tag, c2tag;
if (y1tag == INSIDE) {
c1tag = x1tag;
} else {
c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y+h)) / dy, x, x+w);
}
if (y2tag == INSIDE) {
c2tag = x2tag;
} else {
c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y+h)) / dy, x, x+w);
}
// If the part of the line segment that intersects the Y range
// of the rectangle crosses it horizontally - trivially accept
if (c1tag * c2tag <= 0) {
return true;
}
// Now we know that both the X and Y ranges intersect and that
// the endpoint line segment does not directly cross the rectangle.
//
// We can almost treat this case like one of the cases above
// where both endpoints are to one side, except that we may
// get one or three intersections of the curve with the vertical
// side of the rectangle. This is because the endpoint segment
// accounts for the other intersection in an even pairing. Thus,
// with the endpoint crossing we end up with 2 or 4 total crossings.
//
// (Remember there is overlap in both the X and Y ranges which
// means that the segment itself must cross at least one vertical
// edge of the rectangle - in particular, the "near vertical side"
// - leaving an odd number of intersections for the curve.)
//
// Now we calculate the y tags of all the intersections on the
// "near vertical side" of the rectangle. We will have one with
// the endpoint segment, and one or three with the curve. If
// any pair of those vertical intersections overlap the Y range
// of the rectangle, we have an intersection. Otherwise, we don't.
// c1tag = vertical intersection class of the endpoint segment
//
// Choose the y tag of the endpoint that was not on the same
// side of the rectangle as the subsegment calculated above.
// Note that we can "steal" the existing Y tag of that endpoint
// since it will be provably the same as the vertical intersection.
c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag);
// Now we have to calculate an array of solutions of the curve
// with the "near vertical side" of the rectangle. Then we
// need to sort the tags and do a pairwise range test to see
// if either of the pairs of crossings spans the Y range of
// the rectangle.
//
// Note that the c2tag can still tell us which vertical edge
// to test against.
fillEqn(eqn, (c2tag < INSIDE ? x : x+w), x1, ctrlx1, ctrlx2, x2);
int num = solveCubic(eqn, res);
num = evalCubic(res, num, true, true, null, y1, ctrly1, ctrly2, y2);
// Now put all of the tags into a bucket and sort them. There
// is an intersection iff one of the pairs of tags "spans" the
// Y range of the rectangle.
int tags[] = new int[num+1];
for (int i = 0; i < num; i++) {
tags[i] = getTag(res[i], y, y+h);
}
tags[num] = c1tag;
Arrays.sort(tags);
return ((num >= 1 && tags[0] * tags[1] <= 0) ||
(num >= 3 && tags[2] * tags[3] <= 0));
}
/**
* {@inheritDoc}
*/
@Override
public boolean contains(float x, float y, float w, float h) {
if (w <= 0 || h <= 0) {
return false;
}
// Assertion: Cubic curves closed by connecting their
// endpoints form either one or two convex halves with
// the closing line segment as an edge of both sides.
if (!(contains(x, y) &&
contains(x + w, y) &&
contains(x + w, y + h) &&
contains(x, y + h))) {
return false;
}
// Either the rectangle is entirely inside one of the convex
// halves or it crosses from one to the other, in which case
// it must intersect the closing line segment.
return !Shape.intersectsLine(x, y, w, h, x1, y1, x2, y2);
}
/**
* Returns an iteration object that defines the boundary of the
* shape.
* The iterator for this class is not multi-threaded safe,
* which means that this CubicCurve2D class does not
* guarantee that modifications to the geometry of this
* CubicCurve2D object do not affect any iterations of
* that geometry that are already in process.
* @param tx an optional BaseTransform to be applied to the
* coordinates as they are returned in the iteration, or null
* if untransformed coordinates are desired
* @return the PathIterator object that returns the
* geometry of the outline of this CubicCurve2D, one
* segment at a time.
*/
@Override
public PathIterator getPathIterator(BaseTransform tx) {
return new CubicIterator(this, tx);
}
/**
* Return an iteration object that defines the boundary of the
* flattened shape.
* The iterator for this class is not multi-threaded safe,
* which means that this CubicCurve2D class does not
* guarantee that modifications to the geometry of this
* CubicCurve2D object do not affect any iterations of
* that geometry that are already in process.
* @param tx an optional BaseTransform to be applied to the
* coordinates as they are returned in the iteration, or null
* if untransformed coordinates are desired
* @param flatness the maximum amount that the control points
* for a given curve can vary from colinear before a subdivided
* curve is replaced by a straight line connecting the end points
* @return the PathIterator object that returns the
* geometry of the outline of this CubicCurve2D,
* one segment at a time.
*/
@Override
public PathIterator getPathIterator(BaseTransform tx, float flatness) {
return new FlatteningPathIterator(getPathIterator(tx), flatness);
}
@Override
public CubicCurve2D copy() {
return new CubicCurve2D(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2);
}
@Override
public int hashCode() {
int bits = java.lang.Float.floatToIntBits(x1);
bits += java.lang.Float.floatToIntBits(y1) * 37;
bits += java.lang.Float.floatToIntBits(x2) * 43;
bits += java.lang.Float.floatToIntBits(y2) * 47;
bits += java.lang.Float.floatToIntBits(ctrlx1) * 53;
bits += java.lang.Float.floatToIntBits(ctrly1) * 59;
bits += java.lang.Float.floatToIntBits(ctrlx2) * 61;
bits += java.lang.Float.floatToIntBits(ctrly2) * 101;
return bits;
}
@Override
public boolean equals(Object obj) {
if (obj == this) {
return true;
}
if (obj instanceof CubicCurve2D) {
CubicCurve2D curve = (CubicCurve2D) obj;
return ((x1 == curve.x1) && (y1 == curve.y1) &&
(x2 == curve.x2) && (y2 == curve.y2) &&
(ctrlx1 == curve.ctrlx1) && (ctrly1 == curve.ctrly1) &&
(ctrlx2 == curve.ctrlx2) && (ctrly2 == curve.ctrly2));
}
return false;
}
private float calcX(final float t) {
final float u = 1 - t;
return (u*u*u*x1 +
3*(t*u*u*ctrlx1 +
t*t*u*ctrlx2) +
t*t*t*x2);
}
private float calcY(final float t) {
final float u = 1 - t;
return (u*u*u*y1 +
3*(t*u*u*ctrly1 +
t*t*u*ctrly2) +
t*t*t*y2);
}
}