986 lines
36 KiB
Java
986 lines
36 KiB
Java
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/*
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* Copyright (C) 2007 The Android Open Source Project
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package android.opengl;
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import androidx.annotation.NonNull;
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/**
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* Matrix math utilities. These methods operate on OpenGL ES format
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* matrices and vectors stored in float arrays.
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* <p>
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* Matrices are 4 x 4 column-vector matrices stored in column-major
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* order:
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* <pre>
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* m[offset + 0] m[offset + 4] m[offset + 8] m[offset + 12]
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* m[offset + 1] m[offset + 5] m[offset + 9] m[offset + 13]
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* m[offset + 2] m[offset + 6] m[offset + 10] m[offset + 14]
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* m[offset + 3] m[offset + 7] m[offset + 11] m[offset + 15]</pre>
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*
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* Vectors are 4 x 1 column vectors stored in order:
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* <pre>
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* v[offset + 0]
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* v[offset + 1]
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* v[offset + 2]
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* v[offset + 3]</pre>
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*/
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public class Matrix {
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/** Temporary memory for operations that need temporary matrix data. */
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private static final ThreadLocal<float[]> ThreadTmp = new ThreadLocal() {
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@Override protected float[] initialValue() {
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return new float[32];
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}
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};
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/**
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* @deprecated All methods are static, do not instantiate this class.
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*/
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@Deprecated
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public Matrix() {}
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private static boolean overlap(
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float[] a, int aStart, int aLength, float[] b, int bStart, int bLength) {
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if (a != b) {
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return false;
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}
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if (aStart == bStart) {
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return true;
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}
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int aEnd = aStart + aLength;
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int bEnd = bStart + bLength;
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if (aEnd == bEnd) {
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return true;
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}
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if (aStart < bStart && bStart < aEnd) {
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return true;
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}
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if (aStart < bEnd && bEnd < aEnd) {
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return true;
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}
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if (bStart < aStart && aStart < bEnd) {
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return true;
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}
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if (bStart < aEnd && aEnd < bEnd) {
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return true;
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}
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return false;
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}
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/**
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* Multiplies two 4x4 matrices together and stores the result in a third 4x4
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* matrix. In matrix notation: result = lhs x rhs. Due to the way
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* matrix multiplication works, the result matrix will have the same
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* effect as first multiplying by the rhs matrix, then multiplying by
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* the lhs matrix. This is the opposite of what you might expect.
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* <p>
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* The same float array may be passed for result, lhs, and/or rhs. This
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* operation is expected to do the correct thing if the result elements
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* overlap with either of the lhs or rhs elements.
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*
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* @param result The float array that holds the result.
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* @param resultOffset The offset into the result array where the result is
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* stored.
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* @param lhs The float array that holds the left-hand-side matrix.
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* @param lhsOffset The offset into the lhs array where the lhs is stored
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* @param rhs The float array that holds the right-hand-side matrix.
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* @param rhsOffset The offset into the rhs array where the rhs is stored.
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*
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* @throws IllegalArgumentException under any of the following conditions:
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* result, lhs, or rhs are null;
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* resultOffset + 16 > result.length
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* or lhsOffset + 16 > lhs.length
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* or rhsOffset + 16 > rhs.length;
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* resultOffset < 0 or lhsOffset < 0 or rhsOffset < 0
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*/
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public static void multiplyMM(float[] result, int resultOffset,
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float[] lhs, int lhsOffset, float[] rhs, int rhsOffset) {
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// error checking
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if (result == null) {
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throw new IllegalArgumentException("result == null");
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}
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if (lhs == null) {
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throw new IllegalArgumentException("lhs == null");
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}
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if (rhs == null) {
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throw new IllegalArgumentException("rhs == null");
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}
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if (resultOffset < 0) {
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throw new IllegalArgumentException("resultOffset < 0");
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}
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if (lhsOffset < 0) {
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throw new IllegalArgumentException("lhsOffset < 0");
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}
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if (rhsOffset < 0) {
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throw new IllegalArgumentException("rhsOffset < 0");
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}
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if (result.length < resultOffset + 16) {
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throw new IllegalArgumentException("result.length < resultOffset + 16");
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}
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if (lhs.length < lhsOffset + 16) {
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throw new IllegalArgumentException("lhs.length < lhsOffset + 16");
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}
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if (rhs.length < rhsOffset + 16) {
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throw new IllegalArgumentException("rhs.length < rhsOffset + 16");
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}
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// Check for overlap between rhs and result or lhs and result
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if ( overlap(result, resultOffset, 16, lhs, lhsOffset, 16)
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|| overlap(result, resultOffset, 16, rhs, rhsOffset, 16) ) {
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float[] tmp = ThreadTmp.get();
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for (int i=0; i<4; i++) {
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final float rhs_i0 = rhs[ 4*i + 0 + rhsOffset ];
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float ri0 = lhs[ 0 + lhsOffset ] * rhs_i0;
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float ri1 = lhs[ 1 + lhsOffset ] * rhs_i0;
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float ri2 = lhs[ 2 + lhsOffset ] * rhs_i0;
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float ri3 = lhs[ 3 + lhsOffset ] * rhs_i0;
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for (int j=1; j<4; j++) {
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final float rhs_ij = rhs[ 4*i + j + rhsOffset];
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ri0 += lhs[ 4*j + 0 + lhsOffset ] * rhs_ij;
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ri1 += lhs[ 4*j + 1 + lhsOffset ] * rhs_ij;
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ri2 += lhs[ 4*j + 2 + lhsOffset ] * rhs_ij;
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ri3 += lhs[ 4*j + 3 + lhsOffset ] * rhs_ij;
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}
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tmp[ 4*i + 0 ] = ri0;
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tmp[ 4*i + 1 ] = ri1;
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tmp[ 4*i + 2 ] = ri2;
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tmp[ 4*i + 3 ] = ri3;
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}
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// copy from tmp to result
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for (int i=0; i < 16; i++) {
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result[ i + resultOffset ] = tmp[ i ];
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}
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} else {
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for (int i=0; i<4; i++) {
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final float rhs_i0 = rhs[ 4*i + 0 + rhsOffset ];
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float ri0 = lhs[ 0 + lhsOffset ] * rhs_i0;
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float ri1 = lhs[ 1 + lhsOffset ] * rhs_i0;
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float ri2 = lhs[ 2 + lhsOffset ] * rhs_i0;
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float ri3 = lhs[ 3 + lhsOffset ] * rhs_i0;
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for (int j=1; j<4; j++) {
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final float rhs_ij = rhs[ 4*i + j + rhsOffset];
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ri0 += lhs[ 4*j + 0 + lhsOffset ] * rhs_ij;
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ri1 += lhs[ 4*j + 1 + lhsOffset ] * rhs_ij;
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ri2 += lhs[ 4*j + 2 + lhsOffset ] * rhs_ij;
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ri3 += lhs[ 4*j + 3 + lhsOffset ] * rhs_ij;
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}
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result[ 4*i + 0 + resultOffset ] = ri0;
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result[ 4*i + 1 + resultOffset ] = ri1;
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result[ 4*i + 2 + resultOffset ] = ri2;
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result[ 4*i + 3 + resultOffset ] = ri3;
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}
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}
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}
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/**
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* Multiplies a 4 element vector by a 4x4 matrix and stores the result in a
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* 4-element column vector. In matrix notation: result = lhs x rhs
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* <p>
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* The same float array may be passed for resultVec, lhsMat, and/or rhsVec.
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* This operation is expected to do the correct thing if the result elements
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* overlap with either of the lhs or rhs elements.
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*
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* @param resultVec The float array that holds the result vector.
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* @param resultVecOffset The offset into the result array where the result
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* vector is stored.
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* @param lhsMat The float array that holds the left-hand-side matrix.
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* @param lhsMatOffset The offset into the lhs array where the lhs is stored
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* @param rhsVec The float array that holds the right-hand-side vector.
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* @param rhsVecOffset The offset into the rhs vector where the rhs vector
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* is stored.
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*
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* @throws IllegalArgumentException under any of the following conditions:
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* resultVec, lhsMat, or rhsVec are null;
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* resultVecOffset + 4 > resultVec.length
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* or lhsMatOffset + 16 > lhsMat.length
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* or rhsVecOffset + 4 > rhsVec.length;
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* resultVecOffset < 0 or lhsMatOffset < 0 or rhsVecOffset < 0
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*/
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public static void multiplyMV(float[] resultVec,
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int resultVecOffset, float[] lhsMat, int lhsMatOffset,
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float[] rhsVec, int rhsVecOffset) {
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// error checking
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if (resultVec == null) {
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throw new IllegalArgumentException("resultVec == null");
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}
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if (lhsMat == null) {
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throw new IllegalArgumentException("lhsMat == null");
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}
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if (rhsVec == null) {
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throw new IllegalArgumentException("rhsVec == null");
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}
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if (resultVecOffset < 0) {
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throw new IllegalArgumentException("resultVecOffset < 0");
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}
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if (lhsMatOffset < 0) {
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throw new IllegalArgumentException("lhsMatOffset < 0");
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}
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if (rhsVecOffset < 0) {
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throw new IllegalArgumentException("rhsVecOffset < 0");
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}
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if (resultVec.length < resultVecOffset + 4) {
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throw new IllegalArgumentException("resultVec.length < resultVecOffset + 4");
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}
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if (lhsMat.length < lhsMatOffset + 16) {
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throw new IllegalArgumentException("lhsMat.length < lhsMatOffset + 16");
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}
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if (rhsVec.length < rhsVecOffset + 4) {
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throw new IllegalArgumentException("rhsVec.length < rhsVecOffset + 4");
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}
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float tmp0 = lhsMat[0 + 4 * 0 + lhsMatOffset] * rhsVec[0 + rhsVecOffset] +
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lhsMat[0 + 4 * 1 + lhsMatOffset] * rhsVec[1 + rhsVecOffset] +
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lhsMat[0 + 4 * 2 + lhsMatOffset] * rhsVec[2 + rhsVecOffset] +
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lhsMat[0 + 4 * 3 + lhsMatOffset] * rhsVec[3 + rhsVecOffset];
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float tmp1 = lhsMat[1 + 4 * 0 + lhsMatOffset] * rhsVec[0 + rhsVecOffset] +
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lhsMat[1 + 4 * 1 + lhsMatOffset] * rhsVec[1 + rhsVecOffset] +
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lhsMat[1 + 4 * 2 + lhsMatOffset] * rhsVec[2 + rhsVecOffset] +
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lhsMat[1 + 4 * 3 + lhsMatOffset] * rhsVec[3 + rhsVecOffset];
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float tmp2 = lhsMat[2 + 4 * 0 + lhsMatOffset] * rhsVec[0 + rhsVecOffset] +
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lhsMat[2 + 4 * 1 + lhsMatOffset] * rhsVec[1 + rhsVecOffset] +
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lhsMat[2 + 4 * 2 + lhsMatOffset] * rhsVec[2 + rhsVecOffset] +
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lhsMat[2 + 4 * 3 + lhsMatOffset] * rhsVec[3 + rhsVecOffset];
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float tmp3 = lhsMat[3 + 4 * 0 + lhsMatOffset] * rhsVec[0 + rhsVecOffset] +
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lhsMat[3 + 4 * 1 + lhsMatOffset] * rhsVec[1 + rhsVecOffset] +
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lhsMat[3 + 4 * 2 + lhsMatOffset] * rhsVec[2 + rhsVecOffset] +
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lhsMat[3 + 4 * 3 + lhsMatOffset] * rhsVec[3 + rhsVecOffset];
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resultVec[ 0 + resultVecOffset ] = tmp0;
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resultVec[ 1 + resultVecOffset ] = tmp1;
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resultVec[ 2 + resultVecOffset ] = tmp2;
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resultVec[ 3 + resultVecOffset ] = tmp3;
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}
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/**
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* Transposes a 4 x 4 matrix.
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* <p>
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* mTrans and m must not overlap.
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*
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* @param mTrans the array that holds the output transposed matrix
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* @param mTransOffset an offset into mTrans where the transposed matrix is
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* stored.
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* @param m the input array
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* @param mOffset an offset into m where the input matrix is stored.
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*/
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public static void transposeM(float[] mTrans, int mTransOffset, float[] m,
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int mOffset) {
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for (int i = 0; i < 4; i++) {
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int mBase = i * 4 + mOffset;
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mTrans[i + mTransOffset] = m[mBase];
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mTrans[i + 4 + mTransOffset] = m[mBase + 1];
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mTrans[i + 8 + mTransOffset] = m[mBase + 2];
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mTrans[i + 12 + mTransOffset] = m[mBase + 3];
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}
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}
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/**
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* Inverts a 4 x 4 matrix.
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* <p>
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* mInv and m must not overlap.
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*
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* @param mInv the array that holds the output inverted matrix
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* @param mInvOffset an offset into mInv where the inverted matrix is
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* stored.
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* @param m the input array
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* @param mOffset an offset into m where the input matrix is stored.
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* @return true if the matrix could be inverted, false if it could not.
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*/
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public static boolean invertM(float[] mInv, int mInvOffset, float[] m,
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int mOffset) {
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// Invert a 4 x 4 matrix using Cramer's Rule
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// transpose matrix
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final float src0 = m[mOffset + 0];
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final float src4 = m[mOffset + 1];
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final float src8 = m[mOffset + 2];
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final float src12 = m[mOffset + 3];
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final float src1 = m[mOffset + 4];
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final float src5 = m[mOffset + 5];
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final float src9 = m[mOffset + 6];
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final float src13 = m[mOffset + 7];
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final float src2 = m[mOffset + 8];
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final float src6 = m[mOffset + 9];
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final float src10 = m[mOffset + 10];
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final float src14 = m[mOffset + 11];
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final float src3 = m[mOffset + 12];
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final float src7 = m[mOffset + 13];
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final float src11 = m[mOffset + 14];
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final float src15 = m[mOffset + 15];
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// calculate pairs for first 8 elements (cofactors)
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final float atmp0 = src10 * src15;
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final float atmp1 = src11 * src14;
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||
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final float atmp2 = src9 * src15;
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final float atmp3 = src11 * src13;
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final float atmp4 = src9 * src14;
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final float atmp5 = src10 * src13;
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||
|
|
final float atmp6 = src8 * src15;
|
||
|
|
final float atmp7 = src11 * src12;
|
||
|
|
final float atmp8 = src8 * src14;
|
||
|
|
final float atmp9 = src10 * src12;
|
||
|
|
final float atmp10 = src8 * src13;
|
||
|
|
final float atmp11 = src9 * src12;
|
||
|
|
|
||
|
|
// calculate first 8 elements (cofactors)
|
||
|
|
final float dst0 = (atmp0 * src5 + atmp3 * src6 + atmp4 * src7)
|
||
|
|
- (atmp1 * src5 + atmp2 * src6 + atmp5 * src7);
|
||
|
|
final float dst1 = (atmp1 * src4 + atmp6 * src6 + atmp9 * src7)
|
||
|
|
- (atmp0 * src4 + atmp7 * src6 + atmp8 * src7);
|
||
|
|
final float dst2 = (atmp2 * src4 + atmp7 * src5 + atmp10 * src7)
|
||
|
|
- (atmp3 * src4 + atmp6 * src5 + atmp11 * src7);
|
||
|
|
final float dst3 = (atmp5 * src4 + atmp8 * src5 + atmp11 * src6)
|
||
|
|
- (atmp4 * src4 + atmp9 * src5 + atmp10 * src6);
|
||
|
|
final float dst4 = (atmp1 * src1 + atmp2 * src2 + atmp5 * src3)
|
||
|
|
- (atmp0 * src1 + atmp3 * src2 + atmp4 * src3);
|
||
|
|
final float dst5 = (atmp0 * src0 + atmp7 * src2 + atmp8 * src3)
|
||
|
|
- (atmp1 * src0 + atmp6 * src2 + atmp9 * src3);
|
||
|
|
final float dst6 = (atmp3 * src0 + atmp6 * src1 + atmp11 * src3)
|
||
|
|
- (atmp2 * src0 + atmp7 * src1 + atmp10 * src3);
|
||
|
|
final float dst7 = (atmp4 * src0 + atmp9 * src1 + atmp10 * src2)
|
||
|
|
- (atmp5 * src0 + atmp8 * src1 + atmp11 * src2);
|
||
|
|
|
||
|
|
// calculate pairs for second 8 elements (cofactors)
|
||
|
|
final float btmp0 = src2 * src7;
|
||
|
|
final float btmp1 = src3 * src6;
|
||
|
|
final float btmp2 = src1 * src7;
|
||
|
|
final float btmp3 = src3 * src5;
|
||
|
|
final float btmp4 = src1 * src6;
|
||
|
|
final float btmp5 = src2 * src5;
|
||
|
|
final float btmp6 = src0 * src7;
|
||
|
|
final float btmp7 = src3 * src4;
|
||
|
|
final float btmp8 = src0 * src6;
|
||
|
|
final float btmp9 = src2 * src4;
|
||
|
|
final float btmp10 = src0 * src5;
|
||
|
|
final float btmp11 = src1 * src4;
|
||
|
|
|
||
|
|
// calculate second 8 elements (cofactors)
|
||
|
|
final float dst8 = (btmp0 * src13 + btmp3 * src14 + btmp4 * src15)
|
||
|
|
- (btmp1 * src13 + btmp2 * src14 + btmp5 * src15);
|
||
|
|
final float dst9 = (btmp1 * src12 + btmp6 * src14 + btmp9 * src15)
|
||
|
|
- (btmp0 * src12 + btmp7 * src14 + btmp8 * src15);
|
||
|
|
final float dst10 = (btmp2 * src12 + btmp7 * src13 + btmp10 * src15)
|
||
|
|
- (btmp3 * src12 + btmp6 * src13 + btmp11 * src15);
|
||
|
|
final float dst11 = (btmp5 * src12 + btmp8 * src13 + btmp11 * src14)
|
||
|
|
- (btmp4 * src12 + btmp9 * src13 + btmp10 * src14);
|
||
|
|
final float dst12 = (btmp2 * src10 + btmp5 * src11 + btmp1 * src9 )
|
||
|
|
- (btmp4 * src11 + btmp0 * src9 + btmp3 * src10);
|
||
|
|
final float dst13 = (btmp8 * src11 + btmp0 * src8 + btmp7 * src10)
|
||
|
|
- (btmp6 * src10 + btmp9 * src11 + btmp1 * src8 );
|
||
|
|
final float dst14 = (btmp6 * src9 + btmp11 * src11 + btmp3 * src8 )
|
||
|
|
- (btmp10 * src11 + btmp2 * src8 + btmp7 * src9 );
|
||
|
|
final float dst15 = (btmp10 * src10 + btmp4 * src8 + btmp9 * src9 )
|
||
|
|
- (btmp8 * src9 + btmp11 * src10 + btmp5 * src8 );
|
||
|
|
|
||
|
|
// calculate determinant
|
||
|
|
final float det =
|
||
|
|
src0 * dst0 + src1 * dst1 + src2 * dst2 + src3 * dst3;
|
||
|
|
|
||
|
|
if (det == 0.0f) {
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
// calculate matrix inverse
|
||
|
|
final float invdet = 1.0f / det;
|
||
|
|
mInv[ mInvOffset] = dst0 * invdet;
|
||
|
|
mInv[ 1 + mInvOffset] = dst1 * invdet;
|
||
|
|
mInv[ 2 + mInvOffset] = dst2 * invdet;
|
||
|
|
mInv[ 3 + mInvOffset] = dst3 * invdet;
|
||
|
|
|
||
|
|
mInv[ 4 + mInvOffset] = dst4 * invdet;
|
||
|
|
mInv[ 5 + mInvOffset] = dst5 * invdet;
|
||
|
|
mInv[ 6 + mInvOffset] = dst6 * invdet;
|
||
|
|
mInv[ 7 + mInvOffset] = dst7 * invdet;
|
||
|
|
|
||
|
|
mInv[ 8 + mInvOffset] = dst8 * invdet;
|
||
|
|
mInv[ 9 + mInvOffset] = dst9 * invdet;
|
||
|
|
mInv[10 + mInvOffset] = dst10 * invdet;
|
||
|
|
mInv[11 + mInvOffset] = dst11 * invdet;
|
||
|
|
|
||
|
|
mInv[12 + mInvOffset] = dst12 * invdet;
|
||
|
|
mInv[13 + mInvOffset] = dst13 * invdet;
|
||
|
|
mInv[14 + mInvOffset] = dst14 * invdet;
|
||
|
|
mInv[15 + mInvOffset] = dst15 * invdet;
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Computes an orthographic projection matrix.
|
||
|
|
*
|
||
|
|
* @param m returns the result
|
||
|
|
* @param mOffset
|
||
|
|
* @param left
|
||
|
|
* @param right
|
||
|
|
* @param bottom
|
||
|
|
* @param top
|
||
|
|
* @param near
|
||
|
|
* @param far
|
||
|
|
*/
|
||
|
|
public static void orthoM(float[] m, int mOffset,
|
||
|
|
float left, float right, float bottom, float top,
|
||
|
|
float near, float far) {
|
||
|
|
if (left == right) {
|
||
|
|
throw new IllegalArgumentException("left == right");
|
||
|
|
}
|
||
|
|
if (bottom == top) {
|
||
|
|
throw new IllegalArgumentException("bottom == top");
|
||
|
|
}
|
||
|
|
if (near == far) {
|
||
|
|
throw new IllegalArgumentException("near == far");
|
||
|
|
}
|
||
|
|
|
||
|
|
final float r_width = 1.0f / (right - left);
|
||
|
|
final float r_height = 1.0f / (top - bottom);
|
||
|
|
final float r_depth = 1.0f / (far - near);
|
||
|
|
final float x = 2.0f * (r_width);
|
||
|
|
final float y = 2.0f * (r_height);
|
||
|
|
final float z = -2.0f * (r_depth);
|
||
|
|
final float tx = -(right + left) * r_width;
|
||
|
|
final float ty = -(top + bottom) * r_height;
|
||
|
|
final float tz = -(far + near) * r_depth;
|
||
|
|
m[mOffset + 0] = x;
|
||
|
|
m[mOffset + 5] = y;
|
||
|
|
m[mOffset +10] = z;
|
||
|
|
m[mOffset +12] = tx;
|
||
|
|
m[mOffset +13] = ty;
|
||
|
|
m[mOffset +14] = tz;
|
||
|
|
m[mOffset +15] = 1.0f;
|
||
|
|
m[mOffset + 1] = 0.0f;
|
||
|
|
m[mOffset + 2] = 0.0f;
|
||
|
|
m[mOffset + 3] = 0.0f;
|
||
|
|
m[mOffset + 4] = 0.0f;
|
||
|
|
m[mOffset + 6] = 0.0f;
|
||
|
|
m[mOffset + 7] = 0.0f;
|
||
|
|
m[mOffset + 8] = 0.0f;
|
||
|
|
m[mOffset + 9] = 0.0f;
|
||
|
|
m[mOffset + 11] = 0.0f;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Defines a projection matrix in terms of six clip planes.
|
||
|
|
*
|
||
|
|
* @param m the float array that holds the output perspective matrix
|
||
|
|
* @param offset the offset into float array m where the perspective
|
||
|
|
* matrix data is written
|
||
|
|
* @param left
|
||
|
|
* @param right
|
||
|
|
* @param bottom
|
||
|
|
* @param top
|
||
|
|
* @param near
|
||
|
|
* @param far
|
||
|
|
*/
|
||
|
|
public static void frustumM(float[] m, int offset,
|
||
|
|
float left, float right, float bottom, float top,
|
||
|
|
float near, float far) {
|
||
|
|
if (left == right) {
|
||
|
|
throw new IllegalArgumentException("left == right");
|
||
|
|
}
|
||
|
|
if (top == bottom) {
|
||
|
|
throw new IllegalArgumentException("top == bottom");
|
||
|
|
}
|
||
|
|
if (near == far) {
|
||
|
|
throw new IllegalArgumentException("near == far");
|
||
|
|
}
|
||
|
|
if (near <= 0.0f) {
|
||
|
|
throw new IllegalArgumentException("near <= 0.0f");
|
||
|
|
}
|
||
|
|
if (far <= 0.0f) {
|
||
|
|
throw new IllegalArgumentException("far <= 0.0f");
|
||
|
|
}
|
||
|
|
final float r_width = 1.0f / (right - left);
|
||
|
|
final float r_height = 1.0f / (top - bottom);
|
||
|
|
final float r_depth = 1.0f / (near - far);
|
||
|
|
final float x = 2.0f * (near * r_width);
|
||
|
|
final float y = 2.0f * (near * r_height);
|
||
|
|
final float A = (right + left) * r_width;
|
||
|
|
final float B = (top + bottom) * r_height;
|
||
|
|
final float C = (far + near) * r_depth;
|
||
|
|
final float D = 2.0f * (far * near * r_depth);
|
||
|
|
m[offset + 0] = x;
|
||
|
|
m[offset + 5] = y;
|
||
|
|
m[offset + 8] = A;
|
||
|
|
m[offset + 9] = B;
|
||
|
|
m[offset + 10] = C;
|
||
|
|
m[offset + 14] = D;
|
||
|
|
m[offset + 11] = -1.0f;
|
||
|
|
m[offset + 1] = 0.0f;
|
||
|
|
m[offset + 2] = 0.0f;
|
||
|
|
m[offset + 3] = 0.0f;
|
||
|
|
m[offset + 4] = 0.0f;
|
||
|
|
m[offset + 6] = 0.0f;
|
||
|
|
m[offset + 7] = 0.0f;
|
||
|
|
m[offset + 12] = 0.0f;
|
||
|
|
m[offset + 13] = 0.0f;
|
||
|
|
m[offset + 15] = 0.0f;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Defines a projection matrix in terms of a field of view angle, an
|
||
|
|
* aspect ratio, and z clip planes.
|
||
|
|
*
|
||
|
|
* @param m the float array that holds the perspective matrix
|
||
|
|
* @param offset the offset into float array m where the perspective
|
||
|
|
* matrix data is written
|
||
|
|
* @param fovy field of view in y direction, in degrees
|
||
|
|
* @param aspect width to height aspect ratio of the viewport
|
||
|
|
* @param zNear
|
||
|
|
* @param zFar
|
||
|
|
*/
|
||
|
|
public static void perspectiveM(float[] m, int offset,
|
||
|
|
float fovy, float aspect, float zNear, float zFar) {
|
||
|
|
float f = 1.0f / (float) Math.tan(fovy * (Math.PI / 360.0));
|
||
|
|
float rangeReciprocal = 1.0f / (zNear - zFar);
|
||
|
|
|
||
|
|
m[offset + 0] = f / aspect;
|
||
|
|
m[offset + 1] = 0.0f;
|
||
|
|
m[offset + 2] = 0.0f;
|
||
|
|
m[offset + 3] = 0.0f;
|
||
|
|
|
||
|
|
m[offset + 4] = 0.0f;
|
||
|
|
m[offset + 5] = f;
|
||
|
|
m[offset + 6] = 0.0f;
|
||
|
|
m[offset + 7] = 0.0f;
|
||
|
|
|
||
|
|
m[offset + 8] = 0.0f;
|
||
|
|
m[offset + 9] = 0.0f;
|
||
|
|
m[offset + 10] = (zFar + zNear) * rangeReciprocal;
|
||
|
|
m[offset + 11] = -1.0f;
|
||
|
|
|
||
|
|
m[offset + 12] = 0.0f;
|
||
|
|
m[offset + 13] = 0.0f;
|
||
|
|
m[offset + 14] = 2.0f * zFar * zNear * rangeReciprocal;
|
||
|
|
m[offset + 15] = 0.0f;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Computes the length of a vector.
|
||
|
|
*
|
||
|
|
* @param x x coordinate of a vector
|
||
|
|
* @param y y coordinate of a vector
|
||
|
|
* @param z z coordinate of a vector
|
||
|
|
* @return the length of a vector
|
||
|
|
*/
|
||
|
|
public static float length(float x, float y, float z) {
|
||
|
|
return (float) Math.sqrt(x * x + y * y + z * z);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Sets matrix m to the identity matrix.
|
||
|
|
*
|
||
|
|
* @param sm returns the result
|
||
|
|
* @param smOffset index into sm where the result matrix starts
|
||
|
|
*/
|
||
|
|
public static void setIdentityM(float[] sm, int smOffset) {
|
||
|
|
for (int i=0 ; i<16 ; i++) {
|
||
|
|
sm[smOffset + i] = 0;
|
||
|
|
}
|
||
|
|
for(int i = 0; i < 16; i += 5) {
|
||
|
|
sm[smOffset + i] = 1.0f;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Scales matrix m by x, y, and z, putting the result in sm.
|
||
|
|
* <p>
|
||
|
|
* m and sm must not overlap.
|
||
|
|
*
|
||
|
|
* @param sm returns the result
|
||
|
|
* @param smOffset index into sm where the result matrix starts
|
||
|
|
* @param m source matrix
|
||
|
|
* @param mOffset index into m where the source matrix starts
|
||
|
|
* @param x scale factor x
|
||
|
|
* @param y scale factor y
|
||
|
|
* @param z scale factor z
|
||
|
|
*/
|
||
|
|
public static void scaleM(float[] sm, int smOffset,
|
||
|
|
float[] m, int mOffset,
|
||
|
|
float x, float y, float z) {
|
||
|
|
for (int i=0 ; i<4 ; i++) {
|
||
|
|
int smi = smOffset + i;
|
||
|
|
int mi = mOffset + i;
|
||
|
|
sm[ smi] = m[ mi] * x;
|
||
|
|
sm[ 4 + smi] = m[ 4 + mi] * y;
|
||
|
|
sm[ 8 + smi] = m[ 8 + mi] * z;
|
||
|
|
sm[12 + smi] = m[12 + mi];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Scales matrix m in place by sx, sy, and sz.
|
||
|
|
*
|
||
|
|
* @param m matrix to scale
|
||
|
|
* @param mOffset index into m where the matrix starts
|
||
|
|
* @param x scale factor x
|
||
|
|
* @param y scale factor y
|
||
|
|
* @param z scale factor z
|
||
|
|
*/
|
||
|
|
public static void scaleM(float[] m, int mOffset,
|
||
|
|
float x, float y, float z) {
|
||
|
|
for (int i=0 ; i<4 ; i++) {
|
||
|
|
int mi = mOffset + i;
|
||
|
|
m[ mi] *= x;
|
||
|
|
m[ 4 + mi] *= y;
|
||
|
|
m[ 8 + mi] *= z;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Translates matrix m by x, y, and z, putting the result in tm.
|
||
|
|
* <p>
|
||
|
|
* m and tm must not overlap.
|
||
|
|
*
|
||
|
|
* @param tm returns the result
|
||
|
|
* @param tmOffset index into sm where the result matrix starts
|
||
|
|
* @param m source matrix
|
||
|
|
* @param mOffset index into m where the source matrix starts
|
||
|
|
* @param x translation factor x
|
||
|
|
* @param y translation factor y
|
||
|
|
* @param z translation factor z
|
||
|
|
*/
|
||
|
|
public static void translateM(float[] tm, int tmOffset,
|
||
|
|
float[] m, int mOffset,
|
||
|
|
float x, float y, float z) {
|
||
|
|
for (int i=0 ; i<12 ; i++) {
|
||
|
|
tm[tmOffset + i] = m[mOffset + i];
|
||
|
|
}
|
||
|
|
for (int i=0 ; i<4 ; i++) {
|
||
|
|
int tmi = tmOffset + i;
|
||
|
|
int mi = mOffset + i;
|
||
|
|
tm[12 + tmi] = m[mi] * x + m[4 + mi] * y + m[8 + mi] * z +
|
||
|
|
m[12 + mi];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Translates matrix m by x, y, and z in place.
|
||
|
|
*
|
||
|
|
* @param m matrix
|
||
|
|
* @param mOffset index into m where the matrix starts
|
||
|
|
* @param x translation factor x
|
||
|
|
* @param y translation factor y
|
||
|
|
* @param z translation factor z
|
||
|
|
*/
|
||
|
|
public static void translateM(
|
||
|
|
float[] m, int mOffset,
|
||
|
|
float x, float y, float z) {
|
||
|
|
for (int i=0 ; i<4 ; i++) {
|
||
|
|
int mi = mOffset + i;
|
||
|
|
m[12 + mi] += m[mi] * x + m[4 + mi] * y + m[8 + mi] * z;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Rotates matrix m by angle a (in degrees) around the axis (x, y, z).
|
||
|
|
* <p>
|
||
|
|
* m and rm must not overlap.
|
||
|
|
*
|
||
|
|
* @param rm returns the result
|
||
|
|
* @param rmOffset index into rm where the result matrix starts
|
||
|
|
* @param m source matrix
|
||
|
|
* @param mOffset index into m where the source matrix starts
|
||
|
|
* @param a angle to rotate in degrees
|
||
|
|
* @param x X axis component
|
||
|
|
* @param y Y axis component
|
||
|
|
* @param z Z axis component
|
||
|
|
*/
|
||
|
|
public static void rotateM(float[] rm, int rmOffset,
|
||
|
|
float[] m, int mOffset,
|
||
|
|
float a, float x, float y, float z) {
|
||
|
|
float[] tmp = ThreadTmp.get();
|
||
|
|
setRotateM(tmp, 16, a, x, y, z);
|
||
|
|
multiplyMM(rm, rmOffset, m, mOffset, tmp, 16);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Rotates matrix m in place by angle a (in degrees)
|
||
|
|
* around the axis (x, y, z).
|
||
|
|
*
|
||
|
|
* @param m source matrix
|
||
|
|
* @param mOffset index into m where the matrix starts
|
||
|
|
* @param a angle to rotate in degrees
|
||
|
|
* @param x X axis component
|
||
|
|
* @param y Y axis component
|
||
|
|
* @param z Z axis component
|
||
|
|
*/
|
||
|
|
public static void rotateM(float[] m, int mOffset,
|
||
|
|
float a, float x, float y, float z) {
|
||
|
|
rotateM(m, mOffset, m, mOffset, a, x, y, z);
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Creates a matrix for rotation by angle a (in degrees)
|
||
|
|
* around the axis (x, y, z).
|
||
|
|
* <p>
|
||
|
|
* An optimized path will be used for rotation about a major axis
|
||
|
|
* (e.g. x=1.0f y=0.0f z=0.0f).
|
||
|
|
*
|
||
|
|
* @param rm returns the result
|
||
|
|
* @param rmOffset index into rm where the result matrix starts
|
||
|
|
* @param a angle to rotate in degrees
|
||
|
|
* @param x X axis component
|
||
|
|
* @param y Y axis component
|
||
|
|
* @param z Z axis component
|
||
|
|
*/
|
||
|
|
public static void setRotateM(float[] rm, int rmOffset,
|
||
|
|
float a, float x, float y, float z) {
|
||
|
|
rm[rmOffset + 3] = 0;
|
||
|
|
rm[rmOffset + 7] = 0;
|
||
|
|
rm[rmOffset + 11]= 0;
|
||
|
|
rm[rmOffset + 12]= 0;
|
||
|
|
rm[rmOffset + 13]= 0;
|
||
|
|
rm[rmOffset + 14]= 0;
|
||
|
|
rm[rmOffset + 15]= 1;
|
||
|
|
a *= (float) (Math.PI / 180.0f);
|
||
|
|
float s = (float) Math.sin(a);
|
||
|
|
float c = (float) Math.cos(a);
|
||
|
|
if (1.0f == x && 0.0f == y && 0.0f == z) {
|
||
|
|
rm[rmOffset + 5] = c; rm[rmOffset + 10]= c;
|
||
|
|
rm[rmOffset + 6] = s; rm[rmOffset + 9] = -s;
|
||
|
|
rm[rmOffset + 1] = 0; rm[rmOffset + 2] = 0;
|
||
|
|
rm[rmOffset + 4] = 0; rm[rmOffset + 8] = 0;
|
||
|
|
rm[rmOffset + 0] = 1;
|
||
|
|
} else if (0.0f == x && 1.0f == y && 0.0f == z) {
|
||
|
|
rm[rmOffset + 0] = c; rm[rmOffset + 10]= c;
|
||
|
|
rm[rmOffset + 8] = s; rm[rmOffset + 2] = -s;
|
||
|
|
rm[rmOffset + 1] = 0; rm[rmOffset + 4] = 0;
|
||
|
|
rm[rmOffset + 6] = 0; rm[rmOffset + 9] = 0;
|
||
|
|
rm[rmOffset + 5] = 1;
|
||
|
|
} else if (0.0f == x && 0.0f == y && 1.0f == z) {
|
||
|
|
rm[rmOffset + 0] = c; rm[rmOffset + 5] = c;
|
||
|
|
rm[rmOffset + 1] = s; rm[rmOffset + 4] = -s;
|
||
|
|
rm[rmOffset + 2] = 0; rm[rmOffset + 6] = 0;
|
||
|
|
rm[rmOffset + 8] = 0; rm[rmOffset + 9] = 0;
|
||
|
|
rm[rmOffset + 10]= 1;
|
||
|
|
} else {
|
||
|
|
float len = length(x, y, z);
|
||
|
|
if (1.0f != len) {
|
||
|
|
float recipLen = 1.0f / len;
|
||
|
|
x *= recipLen;
|
||
|
|
y *= recipLen;
|
||
|
|
z *= recipLen;
|
||
|
|
}
|
||
|
|
float nc = 1.0f - c;
|
||
|
|
float xy = x * y;
|
||
|
|
float yz = y * z;
|
||
|
|
float zx = z * x;
|
||
|
|
float xs = x * s;
|
||
|
|
float ys = y * s;
|
||
|
|
float zs = z * s;
|
||
|
|
rm[rmOffset + 0] = x*x*nc + c;
|
||
|
|
rm[rmOffset + 4] = xy*nc - zs;
|
||
|
|
rm[rmOffset + 8] = zx*nc + ys;
|
||
|
|
rm[rmOffset + 1] = xy*nc + zs;
|
||
|
|
rm[rmOffset + 5] = y*y*nc + c;
|
||
|
|
rm[rmOffset + 9] = yz*nc - xs;
|
||
|
|
rm[rmOffset + 2] = zx*nc - ys;
|
||
|
|
rm[rmOffset + 6] = yz*nc + xs;
|
||
|
|
rm[rmOffset + 10] = z*z*nc + c;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Converts Euler angles to a rotation matrix.
|
||
|
|
*
|
||
|
|
* @param rm returns the result
|
||
|
|
* @param rmOffset index into rm where the result matrix starts
|
||
|
|
* @param x angle of rotation, in degrees
|
||
|
|
* @param y is broken, do not use
|
||
|
|
* @param z angle of rotation, in degrees
|
||
|
|
*
|
||
|
|
* @deprecated This method is incorrect around the y axis. This method is
|
||
|
|
* deprecated and replaced (below) by setRotateEulerM2 which
|
||
|
|
* behaves correctly
|
||
|
|
*/
|
||
|
|
@Deprecated
|
||
|
|
public static void setRotateEulerM(float[] rm, int rmOffset,
|
||
|
|
float x, float y, float z) {
|
||
|
|
x *= (float) (Math.PI / 180.0f);
|
||
|
|
y *= (float) (Math.PI / 180.0f);
|
||
|
|
z *= (float) (Math.PI / 180.0f);
|
||
|
|
float cx = (float) Math.cos(x);
|
||
|
|
float sx = (float) Math.sin(x);
|
||
|
|
float cy = (float) Math.cos(y);
|
||
|
|
float sy = (float) Math.sin(y);
|
||
|
|
float cz = (float) Math.cos(z);
|
||
|
|
float sz = (float) Math.sin(z);
|
||
|
|
float cxsy = cx * sy;
|
||
|
|
float sxsy = sx * sy;
|
||
|
|
|
||
|
|
rm[rmOffset + 0] = cy * cz;
|
||
|
|
rm[rmOffset + 1] = -cy * sz;
|
||
|
|
rm[rmOffset + 2] = sy;
|
||
|
|
rm[rmOffset + 3] = 0.0f;
|
||
|
|
|
||
|
|
rm[rmOffset + 4] = cxsy * cz + cx * sz;
|
||
|
|
rm[rmOffset + 5] = -cxsy * sz + cx * cz;
|
||
|
|
rm[rmOffset + 6] = -sx * cy;
|
||
|
|
rm[rmOffset + 7] = 0.0f;
|
||
|
|
|
||
|
|
rm[rmOffset + 8] = -sxsy * cz + sx * sz;
|
||
|
|
rm[rmOffset + 9] = sxsy * sz + sx * cz;
|
||
|
|
rm[rmOffset + 10] = cx * cy;
|
||
|
|
rm[rmOffset + 11] = 0.0f;
|
||
|
|
|
||
|
|
rm[rmOffset + 12] = 0.0f;
|
||
|
|
rm[rmOffset + 13] = 0.0f;
|
||
|
|
rm[rmOffset + 14] = 0.0f;
|
||
|
|
rm[rmOffset + 15] = 1.0f;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Converts Euler angles to a rotation matrix.
|
||
|
|
*
|
||
|
|
* @param rm returns the result
|
||
|
|
* @param rmOffset index into rm where the result matrix starts
|
||
|
|
* @param x angle of rotation, in degrees
|
||
|
|
* @param y angle of rotation, in degrees
|
||
|
|
* @param z angle of rotation, in degrees
|
||
|
|
*
|
||
|
|
* @throws IllegalArgumentException if rm is null;
|
||
|
|
* or if rmOffset + 16 > rm.length;
|
||
|
|
* rmOffset < 0
|
||
|
|
*/
|
||
|
|
public static void setRotateEulerM2(@NonNull float[] rm, int rmOffset,
|
||
|
|
float x, float y, float z) {
|
||
|
|
if (rm == null) {
|
||
|
|
throw new IllegalArgumentException("rm == null");
|
||
|
|
}
|
||
|
|
if (rmOffset < 0) {
|
||
|
|
throw new IllegalArgumentException("rmOffset < 0");
|
||
|
|
}
|
||
|
|
if (rm.length < rmOffset + 16) {
|
||
|
|
throw new IllegalArgumentException("rm.length < rmOffset + 16");
|
||
|
|
}
|
||
|
|
|
||
|
|
x *= (float) (Math.PI / 180.0f);
|
||
|
|
y *= (float) (Math.PI / 180.0f);
|
||
|
|
z *= (float) (Math.PI / 180.0f);
|
||
|
|
float cx = (float) Math.cos(x);
|
||
|
|
float sx = (float) Math.sin(x);
|
||
|
|
float cy = (float) Math.cos(y);
|
||
|
|
float sy = (float) Math.sin(y);
|
||
|
|
float cz = (float) Math.cos(z);
|
||
|
|
float sz = (float) Math.sin(z);
|
||
|
|
float cxsy = cx * sy;
|
||
|
|
float sxsy = sx * sy;
|
||
|
|
|
||
|
|
rm[rmOffset + 0] = cy * cz;
|
||
|
|
rm[rmOffset + 1] = -cy * sz;
|
||
|
|
rm[rmOffset + 2] = sy;
|
||
|
|
rm[rmOffset + 3] = 0.0f;
|
||
|
|
|
||
|
|
rm[rmOffset + 4] = sxsy * cz + cx * sz;
|
||
|
|
rm[rmOffset + 5] = -sxsy * sz + cx * cz;
|
||
|
|
rm[rmOffset + 6] = -sx * cy;
|
||
|
|
rm[rmOffset + 7] = 0.0f;
|
||
|
|
|
||
|
|
rm[rmOffset + 8] = -cxsy * cz + sx * sz;
|
||
|
|
rm[rmOffset + 9] = cxsy * sz + sx * cz;
|
||
|
|
rm[rmOffset + 10] = cx * cy;
|
||
|
|
rm[rmOffset + 11] = 0.0f;
|
||
|
|
|
||
|
|
rm[rmOffset + 12] = 0.0f;
|
||
|
|
rm[rmOffset + 13] = 0.0f;
|
||
|
|
rm[rmOffset + 14] = 0.0f;
|
||
|
|
rm[rmOffset + 15] = 1.0f;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Defines a viewing transformation in terms of an eye point, a center of
|
||
|
|
* view, and an up vector.
|
||
|
|
*
|
||
|
|
* @param rm returns the result
|
||
|
|
* @param rmOffset index into rm where the result matrix starts
|
||
|
|
* @param eyeX eye point X
|
||
|
|
* @param eyeY eye point Y
|
||
|
|
* @param eyeZ eye point Z
|
||
|
|
* @param centerX center of view X
|
||
|
|
* @param centerY center of view Y
|
||
|
|
* @param centerZ center of view Z
|
||
|
|
* @param upX up vector X
|
||
|
|
* @param upY up vector Y
|
||
|
|
* @param upZ up vector Z
|
||
|
|
*/
|
||
|
|
public static void setLookAtM(float[] rm, int rmOffset,
|
||
|
|
float eyeX, float eyeY, float eyeZ,
|
||
|
|
float centerX, float centerY, float centerZ, float upX, float upY,
|
||
|
|
float upZ) {
|
||
|
|
|
||
|
|
// See the OpenGL GLUT documentation for gluLookAt for a description
|
||
|
|
// of the algorithm. We implement it in a straightforward way:
|
||
|
|
|
||
|
|
float fx = centerX - eyeX;
|
||
|
|
float fy = centerY - eyeY;
|
||
|
|
float fz = centerZ - eyeZ;
|
||
|
|
|
||
|
|
// Normalize f
|
||
|
|
float rlf = 1.0f / Matrix.length(fx, fy, fz);
|
||
|
|
fx *= rlf;
|
||
|
|
fy *= rlf;
|
||
|
|
fz *= rlf;
|
||
|
|
|
||
|
|
// compute s = f x up (x means "cross product")
|
||
|
|
float sx = fy * upZ - fz * upY;
|
||
|
|
float sy = fz * upX - fx * upZ;
|
||
|
|
float sz = fx * upY - fy * upX;
|
||
|
|
|
||
|
|
// and normalize s
|
||
|
|
float rls = 1.0f / Matrix.length(sx, sy, sz);
|
||
|
|
sx *= rls;
|
||
|
|
sy *= rls;
|
||
|
|
sz *= rls;
|
||
|
|
|
||
|
|
// compute u = s x f
|
||
|
|
float ux = sy * fz - sz * fy;
|
||
|
|
float uy = sz * fx - sx * fz;
|
||
|
|
float uz = sx * fy - sy * fx;
|
||
|
|
|
||
|
|
rm[rmOffset + 0] = sx;
|
||
|
|
rm[rmOffset + 1] = ux;
|
||
|
|
rm[rmOffset + 2] = -fx;
|
||
|
|
rm[rmOffset + 3] = 0.0f;
|
||
|
|
|
||
|
|
rm[rmOffset + 4] = sy;
|
||
|
|
rm[rmOffset + 5] = uy;
|
||
|
|
rm[rmOffset + 6] = -fy;
|
||
|
|
rm[rmOffset + 7] = 0.0f;
|
||
|
|
|
||
|
|
rm[rmOffset + 8] = sz;
|
||
|
|
rm[rmOffset + 9] = uz;
|
||
|
|
rm[rmOffset + 10] = -fz;
|
||
|
|
rm[rmOffset + 11] = 0.0f;
|
||
|
|
|
||
|
|
rm[rmOffset + 12] = 0.0f;
|
||
|
|
rm[rmOffset + 13] = 0.0f;
|
||
|
|
rm[rmOffset + 14] = 0.0f;
|
||
|
|
rm[rmOffset + 15] = 1.0f;
|
||
|
|
|
||
|
|
translateM(rm, rmOffset, -eyeX, -eyeY, -eyeZ);
|
||
|
|
}
|
||
|
|
}
|