Bezier interpolate
/*
* http://code.google.com/p/ametro/
* Transport map viewer for Android platform
* Copyright (C) 2009-2010 contacts@ametro.org Roman Golovanov and other
* respective project committers (see project home page)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
*/
//package org.ametro.util;
import android.graphics.Point;
import android.graphics.PointF;
import android.graphics.Rect;
class Algorithms {
private final static int LEFT = 1;
private final static int RIGHT = 2;
private final static int TOP = 4;
private final static int BOTTOM = 8;
public static class Solve2x2 {
float __determinant = 0;
public PointF solve(float _a11, float _a12, float _a21, float _a22, float _b1, float _b2, float zeroTolerance, boolean _resolve) {
if (!_resolve) {
__determinant = _a11 * _a22 - _a12 * _a21;
}
// exercise - dispatch an event if the determinant is near zero
if (__determinant > zeroTolerance) {
float x = (_a22 * _b1 - _a12 * _b2) / __determinant;
float y = (_a11 * _b2 - _a21 * _b1) / __determinant;
return new PointF(x, y);
}
return null;
}
}
public static class QBezierControls {
public final float x0;
public final float y0;
public final float x1;
public final float y1;
public QBezierControls(float newX0, float newY0, float newX1, float newY1) {
super();
x0 = newX0;
y0 = newY0;
x1 = newX1;
y1 = newY1;
}
}
public static float calculateDistance(Point p0, Point p1) {
int dx = p0.x - p1.x;
int dy = p0.y - p1.y;
return (float) Math.sqrt(dx * dx + dy * dy);
}
public static float calculateAngle(float x0, float y0, float x, float y) {
float angle = (float) (Math.atan((y - y0) / (x - x0)) / Math.PI * 180);
float dx = x - x0;
float dy = y - y0;
if (angle > 0) {
if (dx < 0 && dy < 0) {
angle += 180;
}
} else if (angle < 0) {
if (dx < 0 && dy > 0) {
angle += 180;
} else {
angle += 360;
}
} else {
if (dx < 0) {
angle = 180;
}
}
return angle;
}
public static PointF interpolateQuadBezier(Point p0, Point p1, Point p2) {
// compute t-value using chord-length parameterization
float dx = p1.x - p0.x;
float dy = p1.y - p0.y;
float d1 = (float) Math.sqrt(dx * dx + dy * dy);
float d = d1;
dx = p2.x - p1.x;
dy = p2.y - p1.y;
d += (float) Math.sqrt(dx * dx + dy * dy);
float t = d1 / d;
float t1 = 1.0f - t;
float tSq = t * t;
float denom = 2.0f * t * t1;
PointF p = new PointF();
p.x = (p1.x - t1 * t1 * p0.x - tSq * p2.x) / denom;
p.y = (p1.y - t1 * t1 * p0.y - tSq * p2.y) / denom;
return p;
}
public static QBezierControls interpolateCubeBezierSmooth(Point p0, Point p1, Point p2, Point p3, float smoothFactor) {
// Assume we need to calculate the control
// points between (x1,y1) and (x2,y2).
// Then x0,y0 - the previous vertex,
// x3,y3 - the next one.
float x0 = p0.x;
float y0 = p0.y;
float x1 = p1.x;
float y1 = p1.y;
float x2 = p2.x;
float y2 = p2.y;
float x3 = p3.x;
float y3 = p3.y;
float xc1 = (x0 + x1) / 2.0f;
float yc1 = (y0 + y1) / 2.0f;
float xc2 = (x1 + x2) / 2.0f;
float yc2 = (y1 + y2) / 2.0f;
float xc3 = (x2 + x3) / 2.0f;
float yc3 = (y2 + y3) / 2.0f;
float len1 = (float) Math.sqrt((x1 - x0) * (x1 - x0) + (y1 - y0) * (y1 - y0));
float len2 = (float) Math.sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
float len3 = (float) Math.sqrt((x3 - x2) * (x3 - x2) + (y3 - y2) * (y3 - y2));
float k1 = len1 / (len1 + len2);
float k2 = len2 / (len2 + len3);
float xm1 = xc1 + (xc2 - xc1) * k1;
float ym1 = yc1 + (yc2 - yc1) * k1;
float xm2 = xc2 + (xc3 - xc2) * k2;
float ym2 = yc2 + (yc3 - yc2) * k2;
float ctrl1_x = xm1 + (xc2 - xm1) * smoothFactor + x1 - xm1;
float ctrl1_y = ym1 + (yc2 - ym1) * smoothFactor + y1 - ym1;
float ctrl2_x = xm2 + (xc2 - xm2) * smoothFactor + x2 - xm2;
float ctrl2_y = ym2 + (yc2 - ym2) * smoothFactor + y2 - ym2;
return new QBezierControls(ctrl1_x, ctrl1_y, ctrl2_x, ctrl2_y);
}
public static int vcode(Rect r, Point p) {
return (((p.x < r.left) ? LEFT : 0) +
((p.x > r.right) ? RIGHT : 0) +
((p.y < r.top) ? TOP : 0) +
((p.y > r.bottom) ? BOTTOM : 0));
}
public static boolean clipCohenSutherland(Rect r, Point a, Point b) {
a = new Point(a);
b = new Point(b);
int code_a, code_b, code;
Point c;
code_a = vcode(r, a);
code_b = vcode(r, b);
while (code_a != 0 || code_b != 0) {
if ((code_a & code_b) != 0)
return false;
if (code_a != 0) {
code = code_a;
c = a;
} else {
code = code_b;
c = b;
}
if ((code & LEFT) != 0) {
c.y += (a.y - b.y) * (r.left - c.x) / (a.x - b.x);
c.x = r.left;
} else if ((code & RIGHT) != 0) {
c.y += (a.y - b.y) * (r.right - c.x) / (a.x - b.x);
c.x = r.right;
}
if ((code & TOP) != 0) {
c.x += (a.x - b.x) * (r.top - c.y) / (a.y - b.y);
c.y = r.top;
} else if ((code & BOTTOM) != 0) {
c.x += (a.x - b.x) * (r.bottom - c.y) / (a.y - b.y);
c.y = r.bottom;
}
if (code == code_a)
code_a = vcode(r, a);
else
code_b = vcode(r, b);
}
return true;
}
public static QBezierControls interpolateCubicBezierControl(Point p0, Point p1, Point p2, Point p3) {
return interpolateCubeBezierSmooth(p0, p1, p2, p3, 1.0f);
// int __p0X = p0.x;
// int __p0Y = p0.y;
// int __p3X = p3.x;
// int __p3Y = p3.y;
//
// // currently, this method auto-parameterizes the curve using chord-length parameterization.
// // A future version might allow inputting the two t-values, but this is more
// // user-friendly (what an over-used term :) As an exercise, try uniform parameterization - t1 = 13/ and 52 = 2/3.
// int deltaX = p1.x - p0.x;
// int deltaY = p1.y - p0.y;
// float d1 = (float)Math.sqrt(deltaX*deltaX + deltaY*deltaY);
//
// deltaX = p2.x - p1.x;
// deltaY = p2.y - p1.y;
// float d2 = (float) Math.sqrt(deltaX*deltaX + deltaY*deltaY);
//
// deltaX = p3.x - p2.x;
// deltaY = p3.y - p2.y;
// float d3 = (float)Math.sqrt(deltaX*deltaX + deltaY*deltaY);
//
// float d = d1 + d2 + d3;
// float __t1 = d1/d;
// float __t2 = (d1+d2)/d;
//
// // there are four unknowns (x- and y-coords for P1 and P2), which are solved as two separate sets of two equations in two unknowns
// float t12 = __t1*__t1;
// float t13 = __t1*t12;
//
// float t22 = __t2*__t2;
// float t23 = __t2*t22;
//
// // x-coordinates of P1 and P2 (t = t1 and t2) - exercise: eliminate redudant
// // computations in these equations
// float a11 = 3*t13 - 6*t12 + 3*__t1;
// float a12 = -3*t13 + 3*t12;
// float a21 = 3*t23 - 6*t22 + 3*__t2;
// float a22 = -3*t23 + 3*t22;
//
// float b1 = -t13*__p3X + __p0X*(t13 - 3*t12 + 3*__t1 -1) + p1.x;
// float b2 = -t23*__p3X + __p0X*(t23 - 3*t22 + 3*__t2 -1) + p2.x;
//
// Solve2x2 s = new Solve2x2();
// PointF p = s.solve(a11, a12, a21, a22, b1, b2, 0, false);
//
// float __p1X = p.x;
// float __p2X = p.y;
//
// // y-coordinates of P1 and P2 (t = t1 and t2)
// b1 = -t13*__p3Y + __p0Y*(t13 - 3*t12 + 3*__t1 -1) + p1.y;
// b2 = -t23*__p3Y + __p0Y*(t23 - 3*t22 + 3*__t2 -1) + p2.y;
//
// // resolving with same coefficients, but new RHS
// p = s.solve(a11, a12, a21, a22, b1, b2, ZERO_TOLERANCE, true);
// float __p1Y = p.x;
// float __p2Y = p.y;
//
// return new QBezierControls(__p1X, __p1Y, __p2X, __p2Y);
}
}
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