mirror of https://github.com/noisymime/Arduino.git
641 lines
19 KiB
Java
641 lines
19 KiB
Java
/* -*- mode: jde; c-basic-offset: 2; indent-tabs-mode: nil -*- */
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/*
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Part of the Processing project - http://Proce55ing.net
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Copyright (c) 2005-06 Ben Fry and Casey Reas
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This library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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This library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General
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Public License along with this library; if not, write to the
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Free Software Foundation, Inc., 59 Temple Place, Suite 330,
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Boston, MA 02111-1307 USA
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*/
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package processing.core;
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/**
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* 4x4 matrix implementation.
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*/
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public final class PMatrix implements PConstants {
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public float m00, m01, m02, m03;
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public float m10, m11, m12, m13;
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public float m20, m21, m22, m23;
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public float m30, m31, m32, m33;
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final static int DEFAULT_STACK_DEPTH = 0;
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int maxStackDepth;
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int stackPointer = 0;
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float stack[][];
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// locally allocated version to avoid creating new memory
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static protected PMatrix inverseCopy;
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public PMatrix() {
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set(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1);
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maxStackDepth = DEFAULT_STACK_DEPTH;
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}
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public PMatrix(int stackDepth) {
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set(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1);
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stack = new float[stackDepth][16];
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maxStackDepth = stackDepth;
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}
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public PMatrix(float m00, float m01, float m02, float m03,
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float m10, float m11, float m12, float m13,
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float m20, float m21, float m22, float m23,
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float m30, float m31, float m32, float m33) {
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set(m00, m01, m02, m03,
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m10, m11, m12, m13,
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m20, m21, m22, m23,
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m30, m31, m32, m33);
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maxStackDepth = DEFAULT_STACK_DEPTH;
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}
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// Make a copy of a matrix. We copy the stack depth,
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// but we don't make a copy of the stack or the stack pointer.
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public PMatrix(PMatrix src) {
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set(src);
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maxStackDepth = src.maxStackDepth;
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stack = new float[maxStackDepth][16];
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}
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public void reset() {
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set(1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 1, 0,
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0, 0, 0, 1);
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}
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public void clearStack() {
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stackPointer = 0;
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}
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public boolean push() {
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if (stackPointer == maxStackDepth) return false;
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stack[stackPointer][0] = m00;
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stack[stackPointer][1] = m01;
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stack[stackPointer][2] = m02;
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stack[stackPointer][3] = m03;
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stack[stackPointer][4] = m10;
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stack[stackPointer][5] = m11;
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stack[stackPointer][6] = m12;
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stack[stackPointer][7] = m13;
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stack[stackPointer][8] = m20;
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stack[stackPointer][9] = m21;
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stack[stackPointer][10] = m22;
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stack[stackPointer][11] = m23;
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stack[stackPointer][12] = m30;
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stack[stackPointer][13] = m31;
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stack[stackPointer][14] = m32;
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stack[stackPointer][15] = m33;
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stackPointer++;
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return true;
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}
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public boolean pop() {
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if (stackPointer == 0) return false;
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stackPointer--;
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m00 = stack[stackPointer][0];
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m01 = stack[stackPointer][1];
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m02 = stack[stackPointer][2];
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m03 = stack[stackPointer][3];
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m10 = stack[stackPointer][4];
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m11 = stack[stackPointer][5];
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m12 = stack[stackPointer][6];
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m13 = stack[stackPointer][7];
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m20 = stack[stackPointer][8];
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m21 = stack[stackPointer][9];
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m22 = stack[stackPointer][10];
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m23 = stack[stackPointer][11];
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m30 = stack[stackPointer][12];
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m31 = stack[stackPointer][13];
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m32 = stack[stackPointer][14];
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m33 = stack[stackPointer][15];
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return true;
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}
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public void set(PMatrix src) {
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set(src.m00, src.m01, src.m02, src.m03,
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src.m10, src.m11, src.m12, src.m13,
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src.m20, src.m21, src.m22, src.m23,
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src.m30, src.m31, src.m32, src.m33);
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}
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public void set(float m00, float m01, float m02, float m03,
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float m10, float m11, float m12, float m13,
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float m20, float m21, float m22, float m23,
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float m30, float m31, float m32, float m33) {
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this.m00 = m00; this.m01 = m01; this.m02 = m02; this.m03 = m03;
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this.m10 = m10; this.m11 = m11; this.m12 = m12; this.m13 = m13;
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this.m20 = m20; this.m21 = m21; this.m22 = m22; this.m23 = m23;
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this.m30 = m30; this.m31 = m31; this.m32 = m32; this.m33 = m33;
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}
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public void translate(float tx, float ty) {
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translate(tx, ty, 0);
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}
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public void invTranslate(float tx, float ty) {
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invTranslate(tx, ty, 0);
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}
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public void translate(float tx, float ty, float tz) {
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m03 += tx*m00 + ty*m01 + tz*m02;
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m13 += tx*m10 + ty*m11 + tz*m12;
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m23 += tx*m20 + ty*m21 + tz*m22;
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m33 += tx*m30 + ty*m31 + tz*m32;
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}
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public void invTranslate(float tx, float ty, float tz) {
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preApply(1, 0, 0, -tx,
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0, 1, 0, -ty,
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0, 0, 1, -tz,
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0, 0, 0, 1);
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}
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// OPT could save several multiplies for the 0s and 1s by just
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// putting the multMatrix code here and removing uneccessary terms
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public void rotateX(float angle) {
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float c = cos(angle);
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float s = sin(angle);
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apply(1, 0, 0, 0, 0, c, -s, 0, 0, s, c, 0, 0, 0, 0, 1);
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}
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public void invRotateX(float angle) {
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float c = cos(-angle);
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float s = sin(-angle);
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preApply(1, 0, 0, 0, 0, c, -s, 0, 0, s, c, 0, 0, 0, 0, 1);
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}
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public void rotateY(float angle) {
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float c = cos(angle);
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float s = sin(angle);
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apply(c, 0, s, 0, 0, 1, 0, 0, -s, 0, c, 0, 0, 0, 0, 1);
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}
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public void invRotateY(float angle) {
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float c = cos(-angle);
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float s = sin(-angle);
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preApply(c, 0, s, 0, 0, 1, 0, 0, -s, 0, c, 0, 0, 0, 0, 1);
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}
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/**
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* Just calls rotateZ because two dimensional rotation
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* is the same as rotating along the z-axis.
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*/
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public void rotate(float angle) {
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rotateZ(angle);
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}
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public void invRotate(float angle) {
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invRotateZ(angle);
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}
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public void rotateZ(float angle) {
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float c = cos(angle);
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float s = sin(angle);
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apply(c, -s, 0, 0, s, c, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1);
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}
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public void invRotateZ(float angle) {
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float c = cos(-angle);
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float s = sin(-angle);
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preApply(c, -s, 0, 0, s, c, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1);
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}
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public void rotate(float angle, float v0, float v1, float v2) {
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// should be in radians (i think), instead of degrees (gl uses degrees)
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// based on 15-463 code, but similar to opengl ref p.443
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// TODO should make sure this vector is normalized
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float c = cos(angle);
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float s = sin(angle);
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float t = 1.0f - c;
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apply((t*v0*v0) + c, (t*v0*v1) - (s*v2), (t*v0*v2) + (s*v1), 0,
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(t*v0*v1) + (s*v2), (t*v1*v1) + c, (t*v1*v2) - (s*v0), 0,
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(t*v0*v2) - (s*v1), (t*v1*v2) + (s*v0), (t*v2*v2) + c, 0,
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0, 0, 0, 1);
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}
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public void invRotate(float angle, float v0, float v1, float v2) {
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// TODO should make sure this vector is normalized
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float c = cos(-angle);
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float s = sin(-angle);
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float t = 1.0f - c;
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preApply((t*v0*v0) + c, (t*v0*v1) - (s*v2), (t*v0*v2) + (s*v1), 0,
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(t*v0*v1) + (s*v2), (t*v1*v1) + c, (t*v1*v2) - (s*v0), 0,
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(t*v0*v2) - (s*v1), (t*v1*v2) + (s*v0), (t*v2*v2) + c, 0,
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0, 0, 0, 1);
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}
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public void scale(float s) {
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apply(s, 0, 0, 0, 0, s, 0, 0, 0, 0, s, 0, 0, 0, 0, 1);
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}
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public void invScale(float s) {
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preApply(1/s, 0, 0, 0, 0, 1/s, 0, 0, 0, 0, 1/s, 0, 0, 0, 0, 1);
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}
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public void scale(float sx, float sy) {
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apply(sx, 0, 0, 0, 0, sy, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1);
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}
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public void invScale(float sx, float sy) {
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preApply(1/sx, 0, 0, 0, 0, 1/sy, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1);
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}
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// OPTIMIZE: same as above
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public void scale(float x, float y, float z) {
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apply(x, 0, 0, 0, 0, y, 0, 0, 0, 0, z, 0, 0, 0, 0, 1);
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}
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public void invScale(float x, float y, float z) {
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preApply(1/x, 0, 0, 0, 0, 1/y, 0, 0, 0, 0, 1/z, 0, 0, 0, 0, 1);
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}
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/*
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public void transform(float n00, float n01, float n02, float n03,
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float n10, float n11, float n12, float n13,
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float n20, float n21, float n22, float n23,
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float n30, float n31, float n32, float n33) {
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apply(n00, n01, n02, n03,
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n10, n11, n12, n13,
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n20, n21, n22, n23,
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n30, n31, n32, n33);
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}
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*/
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public void preApply(PMatrix lhs) {
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preApply(lhs.m00, lhs.m01, lhs.m02, lhs.m03,
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lhs.m10, lhs.m11, lhs.m12, lhs.m13,
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lhs.m20, lhs.m21, lhs.m22, lhs.m23,
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lhs.m30, lhs.m31, lhs.m32, lhs.m33);
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}
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// for inverse operations, like multiplying the matrix on the left
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public void preApply(float n00, float n01, float n02, float n03,
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float n10, float n11, float n12, float n13,
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float n20, float n21, float n22, float n23,
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float n30, float n31, float n32, float n33) {
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float r00 = n00*m00 + n01*m10 + n02*m20 + n03*m30;
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float r01 = n00*m01 + n01*m11 + n02*m21 + n03*m31;
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float r02 = n00*m02 + n01*m12 + n02*m22 + n03*m32;
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float r03 = n00*m03 + n01*m13 + n02*m23 + n03*m33;
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float r10 = n10*m00 + n11*m10 + n12*m20 + n13*m30;
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float r11 = n10*m01 + n11*m11 + n12*m21 + n13*m31;
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float r12 = n10*m02 + n11*m12 + n12*m22 + n13*m32;
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float r13 = n10*m03 + n11*m13 + n12*m23 + n13*m33;
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float r20 = n20*m00 + n21*m10 + n22*m20 + n23*m30;
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float r21 = n20*m01 + n21*m11 + n22*m21 + n23*m31;
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float r22 = n20*m02 + n21*m12 + n22*m22 + n23*m32;
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float r23 = n20*m03 + n21*m13 + n22*m23 + n23*m33;
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float r30 = n30*m00 + n31*m10 + n32*m20 + n33*m30;
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float r31 = n30*m01 + n31*m11 + n32*m21 + n33*m31;
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float r32 = n30*m02 + n31*m12 + n32*m22 + n33*m32;
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float r33 = n30*m03 + n31*m13 + n32*m23 + n33*m33;
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m00 = r00; m01 = r01; m02 = r02; m03 = r03;
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m10 = r10; m11 = r11; m12 = r12; m13 = r13;
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m20 = r20; m21 = r21; m22 = r22; m23 = r23;
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m30 = r30; m31 = r31; m32 = r32; m33 = r33;
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}
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public boolean invApply(PMatrix rhs) {
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PMatrix copy = new PMatrix(rhs);
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PMatrix inverse = copy.invert();
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if (inverse == null) return false;
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preApply(inverse);
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return true;
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}
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public boolean invApply(float n00, float n01, float n02, float n03,
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float n10, float n11, float n12, float n13,
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float n20, float n21, float n22, float n23,
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float n30, float n31, float n32, float n33) {
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if (inverseCopy == null) {
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inverseCopy = new PMatrix();
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}
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inverseCopy.set(n00, n01, n02, n03,
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n10, n11, n12, n13,
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n20, n21, n22, n23,
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n30, n31, n32, n33);
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PMatrix inverse = inverseCopy.invert();
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if (inverse == null) return false;
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preApply(inverse);
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return true;
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}
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public void apply(PMatrix rhs) {
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apply(rhs.m00, rhs.m01, rhs.m02, rhs.m03,
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rhs.m10, rhs.m11, rhs.m12, rhs.m13,
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rhs.m20, rhs.m21, rhs.m22, rhs.m23,
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rhs.m30, rhs.m31, rhs.m32, rhs.m33);
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}
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public void apply(float n00, float n01, float n02, float n03,
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float n10, float n11, float n12, float n13,
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float n20, float n21, float n22, float n23,
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float n30, float n31, float n32, float n33) {
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float r00 = m00*n00 + m01*n10 + m02*n20 + m03*n30;
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float r01 = m00*n01 + m01*n11 + m02*n21 + m03*n31;
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float r02 = m00*n02 + m01*n12 + m02*n22 + m03*n32;
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float r03 = m00*n03 + m01*n13 + m02*n23 + m03*n33;
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float r10 = m10*n00 + m11*n10 + m12*n20 + m13*n30;
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float r11 = m10*n01 + m11*n11 + m12*n21 + m13*n31;
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float r12 = m10*n02 + m11*n12 + m12*n22 + m13*n32;
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float r13 = m10*n03 + m11*n13 + m12*n23 + m13*n33;
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float r20 = m20*n00 + m21*n10 + m22*n20 + m23*n30;
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float r21 = m20*n01 + m21*n11 + m22*n21 + m23*n31;
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float r22 = m20*n02 + m21*n12 + m22*n22 + m23*n32;
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float r23 = m20*n03 + m21*n13 + m22*n23 + m23*n33;
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float r30 = m30*n00 + m31*n10 + m32*n20 + m33*n30;
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float r31 = m30*n01 + m31*n11 + m32*n21 + m33*n31;
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float r32 = m30*n02 + m31*n12 + m32*n22 + m33*n32;
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float r33 = m30*n03 + m31*n13 + m32*n23 + m33*n33;
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m00 = r00; m01 = r01; m02 = r02; m03 = r03;
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m10 = r10; m11 = r11; m12 = r12; m13 = r13;
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m20 = r20; m21 = r21; m22 = r22; m23 = r23;
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m30 = r30; m31 = r31; m32 = r32; m33 = r33;
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}
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public void mult3(float vec[], float out[]) {
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// must use these temp vars because vec may be the same as out
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float tmpx = m00*vec[0] + m01*vec[1] + m02*vec[2] + m03;
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float tmpy = m10*vec[0] + m11*vec[1] + m12*vec[2] + m13;
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float tmpz = m20*vec[0] + m21*vec[1] + m22*vec[2] + m23;
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out[0] = tmpx;
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out[1] = tmpy;
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out[2] = tmpz;
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}
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public void mult(float vec[], float out[]) {
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// must use these temp vars because vec may be the same as out
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float tmpx = m00*vec[0] + m01*vec[1] + m02*vec[2] + m03*vec[3];
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float tmpy = m10*vec[0] + m11*vec[1] + m12*vec[2] + m13*vec[3];
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float tmpz = m20*vec[0] + m21*vec[1] + m22*vec[2] + m23*vec[3];
|
|
float tmpw = m30*vec[0] + m31*vec[1] + m32*vec[2] + m33*vec[3];
|
|
|
|
out[0] = tmpx;
|
|
out[1] = tmpy;
|
|
out[2] = tmpz;
|
|
out[3] = tmpw;
|
|
}
|
|
|
|
|
|
/**
|
|
* @return the determinant of the matrix
|
|
*/
|
|
public float determinant() {
|
|
float f =
|
|
m00
|
|
* ((m11 * m22 * m33 + m12 * m23 * m31 + m13 * m21 * m32)
|
|
- m13 * m22 * m31
|
|
- m11 * m23 * m32
|
|
- m12 * m21 * m33);
|
|
f -= m01
|
|
* ((m10 * m22 * m33 + m12 * m23 * m30 + m13 * m20 * m32)
|
|
- m13 * m22 * m30
|
|
- m10 * m23 * m32
|
|
- m12 * m20 * m33);
|
|
f += m02
|
|
* ((m10 * m21 * m33 + m11 * m23 * m30 + m13 * m20 * m31)
|
|
- m13 * m21 * m30
|
|
- m10 * m23 * m31
|
|
- m11 * m20 * m33);
|
|
f -= m03
|
|
* ((m10 * m21 * m32 + m11 * m22 * m30 + m12 * m20 * m31)
|
|
- m12 * m21 * m30
|
|
- m10 * m22 * m31
|
|
- m11 * m20 * m32);
|
|
return f;
|
|
}
|
|
|
|
|
|
/**
|
|
* Calculate the determinant of a 3x3 matrix
|
|
* @return result
|
|
*/
|
|
private float determinant3x3(float t00, float t01, float t02,
|
|
float t10, float t11, float t12,
|
|
float t20, float t21, float t22) {
|
|
return (t00 * (t11 * t22 - t12 * t21) +
|
|
t01 * (t12 * t20 - t10 * t22) +
|
|
t02 * (t10 * t21 - t11 * t20));
|
|
}
|
|
|
|
|
|
public PMatrix transpose() {
|
|
float temp;
|
|
temp = m01; m01 = m10; m10 = temp;
|
|
temp = m02; m02 = m20; m20 = temp;
|
|
temp = m03; m03 = m30; m30 = temp;
|
|
temp = m12; m12 = m21; m21 = temp;
|
|
temp = m13; m13 = m31; m31 = temp;
|
|
temp = m23; m23 = m32; m32 = temp;
|
|
return this;
|
|
}
|
|
|
|
|
|
/**
|
|
* Invert this matrix
|
|
* @return this if successful, null otherwise
|
|
*/
|
|
public PMatrix invert() {
|
|
|
|
float determinant = determinant();
|
|
|
|
if (determinant != 0) {
|
|
// m00 m01 m02 m03
|
|
// m10 m11 m12 m13
|
|
// m20 m21 m22 m23
|
|
// m30 m31 m32 m33
|
|
float determinant_inv = 1f / determinant;
|
|
|
|
// first row
|
|
float t00 = determinant3x3(m11, m12, m13, m21, m22, m23, m31, m32, m33);
|
|
float t01 = -determinant3x3(m10, m12, m13, m20, m22, m23, m30, m32, m33);
|
|
float t02 = determinant3x3(m10, m11, m13, m20, m21, m23, m30, m31, m33);
|
|
float t03 = -determinant3x3(m10, m11, m12, m20, m21, m22, m30, m31, m32);
|
|
|
|
// second row
|
|
float t10 = -determinant3x3(m01, m02, m03, m21, m22, m23, m31, m32, m33);
|
|
float t11 = determinant3x3(m00, m02, m03, m20, m22, m23, m30, m32, m33);
|
|
float t12 = -determinant3x3(m00, m01, m03, m20, m21, m23, m30, m31, m33);
|
|
float t13 = determinant3x3(m00, m01, m02, m20, m21, m22, m30, m31, m32);
|
|
|
|
// third row
|
|
float t20 = determinant3x3(m01, m02, m03, m11, m12, m13, m31, m32, m33);
|
|
float t21 = -determinant3x3(m00, m02, m03, m10, m12, m13, m30, m32, m33);
|
|
float t22 = determinant3x3(m00, m01, m03, m10, m11, m13, m30, m31, m33);
|
|
float t23 = -determinant3x3(m00, m01, m02, m10, m11, m12, m30, m31, m32);
|
|
|
|
// fourth row
|
|
float t30 = -determinant3x3(m01, m02, m03, m11, m12, m13, m21, m22, m23);
|
|
float t31 = determinant3x3(m00, m02, m03, m10, m12, m13, m20, m22, m23);
|
|
float t32 = -determinant3x3(m00, m01, m03, m10, m11, m13, m20, m21, m23);
|
|
float t33 = determinant3x3(m00, m01, m02, m10, m11, m12, m20, m21, m22);
|
|
|
|
// transpose and divide by the determinant
|
|
m00 = t00*determinant_inv;
|
|
m11 = t11*determinant_inv;
|
|
m22 = t22*determinant_inv;
|
|
m33 = t33*determinant_inv;
|
|
m01 = t10*determinant_inv;
|
|
m10 = t01*determinant_inv;
|
|
m20 = t02*determinant_inv;
|
|
m02 = t20*determinant_inv;
|
|
m12 = t21*determinant_inv;
|
|
m21 = t12*determinant_inv;
|
|
m03 = t30*determinant_inv;
|
|
m30 = t03*determinant_inv;
|
|
m13 = t31*determinant_inv;
|
|
m31 = t13*determinant_inv;
|
|
m32 = t23*determinant_inv;
|
|
m23 = t32*determinant_inv;
|
|
return this;
|
|
}
|
|
return null;
|
|
}
|
|
|
|
|
|
//////////////////////////////////////////////////////////////
|
|
|
|
|
|
public void print() {
|
|
int big = (int) Math.abs(max(max(max(max(abs(m00), abs(m01)),
|
|
max(abs(m02), abs(m03))),
|
|
max(max(abs(m10), abs(m11)),
|
|
max(abs(m12), abs(m13)))),
|
|
max(max(max(abs(m20), abs(m21)),
|
|
max(abs(m22), abs(m23))),
|
|
max(max(abs(m30), abs(m31)),
|
|
max(abs(m32), abs(m33))))));
|
|
|
|
// avoid infinite loop
|
|
if (Float.isNaN(big) || Float.isInfinite(big)) {
|
|
big = 1000000; // set to something arbitrary
|
|
}
|
|
|
|
int d = 1;
|
|
while ((big /= 10) != 0) d++; // cheap log()
|
|
|
|
System.out.println(PApplet.nfs(m00, d, 4) + " " +
|
|
PApplet.nfs(m01, d, 4) + " " +
|
|
PApplet.nfs(m02, d, 4) + " " +
|
|
PApplet.nfs(m03, d, 4));
|
|
|
|
System.out.println(PApplet.nfs(m10, d, 4) + " " +
|
|
PApplet.nfs(m11, d, 4) + " " +
|
|
PApplet.nfs(m12, d, 4) + " " +
|
|
PApplet.nfs(m13, d, 4));
|
|
|
|
System.out.println(PApplet.nfs(m20, d, 4) + " " +
|
|
PApplet.nfs(m21, d, 4) + " " +
|
|
PApplet.nfs(m22, d, 4) + " " +
|
|
PApplet.nfs(m23, d, 4));
|
|
|
|
System.out.println(PApplet.nfs(m30, d, 4) + " " +
|
|
PApplet.nfs(m31, d, 4) + " " +
|
|
PApplet.nfs(m32, d, 4) + " " +
|
|
PApplet.nfs(m33, d, 4));
|
|
|
|
System.out.println();
|
|
}
|
|
|
|
|
|
//////////////////////////////////////////////////////////////
|
|
|
|
|
|
private final float max(float a, float b) {
|
|
return (a > b) ? a : b;
|
|
}
|
|
|
|
private final float abs(float a) {
|
|
return (a < 0) ? -a : a;
|
|
}
|
|
|
|
private final float sin(float angle) {
|
|
return (float)Math.sin(angle);
|
|
}
|
|
|
|
private final float cos(float angle) {
|
|
return (float)Math.cos(angle);
|
|
}
|
|
}
|