42e1e0d482
Avoid using textures for common gradients (two stops from 0.0 to 1.0) Change-Id: Iff55d21b126c8cfc4cfb701669f2339c8f6b131a
726 lines
26 KiB
Java
726 lines
26 KiB
Java
/*
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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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/**
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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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*
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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]
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* </pre>
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*
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* Vectors are 4 row x 1 column 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]
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* </pre>
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*
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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 final static float[] sTemp = new float[32];
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/**
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* Multiply two 4x4 matrices together and store 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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*
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* The same float array may be passed for result, lhs, and/or rhs. However,
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* the result element values are undefined if the result elements overlap
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* either 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 if result, lhs, or rhs are null, or if
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* resultOffset + 16 > result.length or lhsOffset + 16 > lhs.length or
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* rhsOffset + 16 > rhs.length.
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*/
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public static native void multiplyMM(float[] result, int resultOffset,
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float[] lhs, int lhsOffset, float[] rhs, int rhsOffset);
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/**
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* Multiply a 4 element vector by a 4x4 matrix and store the result in a 4
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* element column vector. In matrix notation: result = lhs x rhs
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*
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* The same float array may be passed for resultVec, lhsMat, and/or rhsVec.
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* However, the resultVec element values are undefined if the resultVec
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* elements overlap either the lhsMat or rhsVec 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 if resultVec, lhsMat,
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* or rhsVec are null, or if resultVecOffset + 4 > resultVec.length
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* or lhsMatOffset + 16 > lhsMat.length or
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* rhsVecOffset + 4 > rhsVec.length.
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*/
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public static native 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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/**
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* Transposes a 4 x 4 matrix.
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*
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* @param mTrans the array that holds the output inverted matrix
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* @param mTransOffset 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 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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*
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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 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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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;
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final float atmp7 = src11 * src12;
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final float atmp8 = src8 * src14;
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final float atmp9 = src10 * src12;
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final float atmp10 = src8 * src13;
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final float atmp11 = src9 * src12;
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// calculate first 8 elements (cofactors)
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final float dst0 = (atmp0 * src5 + atmp3 * src6 + atmp4 * src7)
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- (atmp1 * src5 + atmp2 * src6 + atmp5 * src7);
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final float dst1 = (atmp1 * src4 + atmp6 * src6 + atmp9 * src7)
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- (atmp0 * src4 + atmp7 * src6 + atmp8 * src7);
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final float dst2 = (atmp2 * src4 + atmp7 * src5 + atmp10 * src7)
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- (atmp3 * src4 + atmp6 * src5 + atmp11 * src7);
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final float dst3 = (atmp5 * src4 + atmp8 * src5 + atmp11 * src6)
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- (atmp4 * src4 + atmp9 * src5 + atmp10 * src6);
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final float dst4 = (atmp1 * src1 + atmp2 * src2 + atmp5 * src3)
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- (atmp0 * src1 + atmp3 * src2 + atmp4 * src3);
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final float dst5 = (atmp0 * src0 + atmp7 * src2 + atmp8 * src3)
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- (atmp1 * src0 + atmp6 * src2 + atmp9 * src3);
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final float dst6 = (atmp3 * src0 + atmp6 * src1 + atmp11 * src3)
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- (atmp2 * src0 + atmp7 * src1 + atmp10 * src3);
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final float dst7 = (atmp4 * src0 + atmp9 * src1 + atmp10 * src2)
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- (atmp5 * src0 + atmp8 * src1 + atmp11 * src2);
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// calculate pairs for second 8 elements (cofactors)
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final float btmp0 = src2 * src7;
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final float btmp1 = src3 * src6;
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final float btmp2 = src1 * src7;
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final float btmp3 = src3 * src5;
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final float btmp4 = src1 * src6;
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final float btmp5 = src2 * src5;
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final float btmp6 = src0 * src7;
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final float btmp7 = src3 * src4;
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final float btmp8 = src0 * src6;
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final float btmp9 = src2 * src4;
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final float btmp10 = src0 * src5;
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final float btmp11 = src1 * src4;
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// calculate second 8 elements (cofactors)
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final float dst8 = (btmp0 * src13 + btmp3 * src14 + btmp4 * src15)
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- (btmp1 * src13 + btmp2 * src14 + btmp5 * src15);
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final float dst9 = (btmp1 * src12 + btmp6 * src14 + btmp9 * src15)
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- (btmp0 * src12 + btmp7 * src14 + btmp8 * src15);
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final float dst10 = (btmp2 * src12 + btmp7 * src13 + btmp10 * src15)
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- (btmp3 * src12 + btmp6 * src13 + btmp11 * src15);
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final float dst11 = (btmp5 * src12 + btmp8 * src13 + btmp11 * src14)
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- (btmp4 * src12 + btmp9 * src13 + btmp10 * src14);
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final float dst12 = (btmp2 * src10 + btmp5 * src11 + btmp1 * src9 )
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- (btmp4 * src11 + btmp0 * src9 + btmp3 * src10);
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final float dst13 = (btmp8 * src11 + btmp0 * src8 + btmp7 * src10)
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- (btmp6 * src10 + btmp9 * src11 + btmp1 * src8 );
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final float dst14 = (btmp6 * src9 + btmp11 * src11 + btmp3 * src8 )
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- (btmp10 * src11 + btmp2 * src8 + btmp7 * src9 );
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final float dst15 = (btmp10 * src10 + btmp4 * src8 + btmp9 * src9 )
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- (btmp8 * src9 + btmp11 * src10 + btmp5 * src8 );
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// calculate determinant
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final float det =
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src0 * dst0 + src1 * dst1 + src2 * dst2 + src3 * dst3;
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if (det == 0.0f) {
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return false;
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}
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// calculate matrix inverse
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final float invdet = 1.0f / det;
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mInv[ mInvOffset] = dst0 * invdet;
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mInv[ 1 + mInvOffset] = dst1 * invdet;
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mInv[ 2 + mInvOffset] = dst2 * invdet;
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mInv[ 3 + mInvOffset] = dst3 * invdet;
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mInv[ 4 + mInvOffset] = dst4 * invdet;
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mInv[ 5 + mInvOffset] = dst5 * invdet;
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mInv[ 6 + mInvOffset] = dst6 * invdet;
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mInv[ 7 + mInvOffset] = dst7 * invdet;
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mInv[ 8 + mInvOffset] = dst8 * invdet;
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mInv[ 9 + mInvOffset] = dst9 * invdet;
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mInv[10 + mInvOffset] = dst10 * invdet;
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mInv[11 + mInvOffset] = dst11 * invdet;
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mInv[12 + mInvOffset] = dst12 * invdet;
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mInv[13 + mInvOffset] = dst13 * invdet;
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mInv[14 + mInvOffset] = dst14 * invdet;
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mInv[15 + mInvOffset] = dst15 * invdet;
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return true;
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}
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/**
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* Computes an orthographic projection matrix.
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*
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* @param m returns the result
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* @param mOffset
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* @param left
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* @param right
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* @param bottom
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* @param top
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* @param near
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* @param far
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*/
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public static void orthoM(float[] m, int mOffset,
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float left, float right, float bottom, float top,
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float near, float far) {
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if (left == right) {
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throw new IllegalArgumentException("left == right");
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}
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if (bottom == top) {
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throw new IllegalArgumentException("bottom == top");
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}
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if (near == far) {
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throw new IllegalArgumentException("near == far");
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}
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final float r_width = 1.0f / (right - left);
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final float r_height = 1.0f / (top - bottom);
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final float r_depth = 1.0f / (far - near);
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final float x = 2.0f * (r_width);
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final float y = 2.0f * (r_height);
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final float z = -2.0f * (r_depth);
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final float tx = -(right + left) * r_width;
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final float ty = -(top + bottom) * r_height;
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final float tz = -(far + near) * r_depth;
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m[mOffset + 0] = x;
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m[mOffset + 5] = y;
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m[mOffset +10] = z;
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m[mOffset +12] = tx;
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m[mOffset +13] = ty;
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m[mOffset +14] = tz;
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m[mOffset +15] = 1.0f;
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m[mOffset + 1] = 0.0f;
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m[mOffset + 2] = 0.0f;
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m[mOffset + 3] = 0.0f;
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m[mOffset + 4] = 0.0f;
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m[mOffset + 6] = 0.0f;
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m[mOffset + 7] = 0.0f;
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m[mOffset + 8] = 0.0f;
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m[mOffset + 9] = 0.0f;
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m[mOffset + 11] = 0.0f;
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}
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/**
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* Define a projection matrix in terms of six clip planes
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* @param m the float array that holds the perspective matrix
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* @param offset the offset into float array m where the perspective
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* matrix data is written
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* @param left
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* @param right
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* @param bottom
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* @param top
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* @param near
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* @param far
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*/
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public static void frustumM(float[] m, int offset,
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float left, float right, float bottom, float top,
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float near, float far) {
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if (left == right) {
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throw new IllegalArgumentException("left == right");
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}
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if (top == bottom) {
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throw new IllegalArgumentException("top == bottom");
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}
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if (near == far) {
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throw new IllegalArgumentException("near == far");
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}
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if (near <= 0.0f) {
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throw new IllegalArgumentException("near <= 0.0f");
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}
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if (far <= 0.0f) {
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throw new IllegalArgumentException("far <= 0.0f");
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}
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final float r_width = 1.0f / (right - left);
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final float r_height = 1.0f / (top - bottom);
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final float r_depth = 1.0f / (near - far);
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final float x = 2.0f * (near * r_width);
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final float y = 2.0f * (near * r_height);
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final float A = (right + left) * r_width;
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final float B = (top + bottom) * r_height;
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final float C = (far + near) * r_depth;
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final float D = 2.0f * (far * near * r_depth);
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m[offset + 0] = x;
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m[offset + 5] = y;
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m[offset + 8] = A;
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m[offset + 9] = B;
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m[offset + 10] = C;
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m[offset + 14] = D;
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m[offset + 11] = -1.0f;
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m[offset + 1] = 0.0f;
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m[offset + 2] = 0.0f;
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m[offset + 3] = 0.0f;
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m[offset + 4] = 0.0f;
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m[offset + 6] = 0.0f;
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m[offset + 7] = 0.0f;
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m[offset + 12] = 0.0f;
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m[offset + 13] = 0.0f;
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m[offset + 15] = 0.0f;
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}
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/**
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* Define a projection matrix in terms of a field of view angle, an
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* aspect ratio, and z clip planes
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* @param m the float array that holds the perspective matrix
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* @param offset the offset into float array m where the perspective
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* matrix data is written
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* @param fovy field of view in y direction, in degrees
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* @param aspect width to height aspect ratio of the viewport
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* @param zNear
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* @param zFar
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*/
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public static void perspectiveM(float[] m, int offset,
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float fovy, float aspect, float zNear, float zFar) {
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float f = 1.0f / (float) Math.tan(fovy * (Math.PI / 360.0));
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float rangeReciprocal = 1.0f / (zNear - zFar);
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m[offset + 0] = f / aspect;
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m[offset + 1] = 0.0f;
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m[offset + 2] = 0.0f;
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m[offset + 3] = 0.0f;
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m[offset + 4] = 0.0f;
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m[offset + 5] = f;
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m[offset + 6] = 0.0f;
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m[offset + 7] = 0.0f;
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m[offset + 8] = 0.0f;
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m[offset + 9] = 0.0f;
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m[offset + 10] = (zFar + zNear) * rangeReciprocal;
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m[offset + 11] = -1.0f;
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m[offset + 12] = 0.0f;
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m[offset + 13] = 0.0f;
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m[offset + 14] = 2.0f * zFar * zNear * rangeReciprocal;
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m[offset + 15] = 0.0f;
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}
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/**
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* Computes the length of a vector
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*
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* @param x x coordinate of a vector
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* @param y y coordinate of a vector
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* @param z z coordinate of a vector
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* @return the length of a vector
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*/
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public static float length(float x, float y, float z) {
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return (float) Math.sqrt(x * x + y * y + z * z);
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}
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/**
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* Sets matrix m to the identity matrix.
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* @param sm returns the result
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* @param smOffset index into sm where the result matrix starts
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*/
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public static void setIdentityM(float[] sm, int smOffset) {
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for (int i=0 ; i<16 ; i++) {
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sm[smOffset + i] = 0;
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}
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for(int i = 0; i < 16; i += 5) {
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sm[smOffset + i] = 1.0f;
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}
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}
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/**
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* Scales matrix m by x, y, and z, putting the result in sm
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* @param sm returns the result
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* @param smOffset index into sm where the result matrix starts
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* @param m source matrix
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* @param mOffset index into m where the source matrix starts
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* @param x scale factor x
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* @param y scale factor y
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* @param z scale factor z
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*/
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public static void scaleM(float[] sm, int smOffset,
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float[] m, int mOffset,
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float x, float y, float z) {
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for (int i=0 ; i<4 ; i++) {
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int smi = smOffset + i;
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int mi = mOffset + i;
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sm[ smi] = m[ mi] * x;
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sm[ 4 + smi] = m[ 4 + mi] * y;
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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
|
|
* @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)
|
|
* @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 scale factor x
|
|
* @param y scale factor y
|
|
* @param z scale factor z
|
|
*/
|
|
public static void rotateM(float[] rm, int rmOffset,
|
|
float[] m, int mOffset,
|
|
float a, float x, float y, float z) {
|
|
synchronized(sTemp) {
|
|
setRotateM(sTemp, 0, a, x, y, z);
|
|
multiplyMM(rm, rmOffset, m, mOffset, sTemp, 0);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* 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 scale factor x
|
|
* @param y scale factor y
|
|
* @param z scale factor z
|
|
*/
|
|
public static void rotateM(float[] m, int mOffset,
|
|
float a, float x, float y, float z) {
|
|
synchronized(sTemp) {
|
|
setRotateM(sTemp, 0, a, x, y, z);
|
|
multiplyMM(sTemp, 16, m, mOffset, sTemp, 0);
|
|
System.arraycopy(sTemp, 16, m, mOffset, 16);
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Rotates matrix m by angle a (in degrees) around the axis (x, y, z)
|
|
* @param rm returns the result
|
|
* @param rmOffset index into rm where the result matrix starts
|
|
* @param a angle to rotate in degrees
|
|
* @param x scale factor x
|
|
* @param y scale factor y
|
|
* @param z scale factor z
|
|
*/
|
|
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 angle of rotation, in degrees
|
|
* @param z angle of rotation, in degrees
|
|
*/
|
|
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;
|
|
}
|
|
|
|
/**
|
|
* Define 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);
|
|
}
|
|
}
|