/* * Copyright 2023 The Android Open Source Project * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ package android.graphics; import android.annotation.FlaggedApi; import android.annotation.IntRange; import android.annotation.NonNull; import com.android.graphics.hwui.flags.Flags; import java.util.Arrays; /** * The Matrix44 class holds a 4x4 matrix for transforming coordinates. It is similar to * {@link Matrix}, and should be used when you want to manipulate the canvas in 3D. Values are kept * in row-major order. The values and operations are treated as column vectors. */ @FlaggedApi(Flags.FLAG_MATRIX_44) public class Matrix44 { final float[] mBackingArray; /** * The default Matrix44 constructor will instantiate an identity matrix. */ @FlaggedApi(Flags.FLAG_MATRIX_44) public Matrix44() { mBackingArray = new float[]{1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f}; } /** * Creates and returns a Matrix44 by taking the 3x3 Matrix and placing it on the 0 of the z-axis * by setting row {@code 2} and column {@code 2} to the identity as seen in the following * operation: *
* [ a b c ] [ a b 0 c ] * [ d e f ] -> [ d e 0 f ] * [ g h i ] [ 0 0 1 0 ] * [ g h 0 i ] ** * @param mat A 3x3 Matrix to be converted (original Matrix will not be changed) */ @FlaggedApi(Flags.FLAG_MATRIX_44) public Matrix44(@NonNull Matrix mat) { float[] m = new float[9]; mat.getValues(m); mBackingArray = new float[]{m[0], m[1], 0.0f, m[2], m[3], m[4], 0.0f, m[5], 0.0f, 0.0f, 1.0f, 0.0f, m[6], m[7], 0.0f, m[8]}; } /** * Copies matrix values into the provided array in row-major order. * * @param dst The float array where values will be copied, must be of length 16 * @throws IllegalArgumentException if the destination float array is not of length 16 */ @FlaggedApi(Flags.FLAG_MATRIX_44) public void getValues(@NonNull float [] dst) { if (dst.length == 16) { System.arraycopy(mBackingArray, 0, dst, 0, mBackingArray.length); } else { throw new IllegalArgumentException("Dst array must be of length 16"); } } /** * Replaces the Matrix's values with the values in the provided array. * * @param src A float array of length 16. Floats are treated in row-major order * @throws IllegalArgumentException if the destination float array is not of length 16 */ @FlaggedApi(Flags.FLAG_MATRIX_44) public void setValues(@NonNull float[] src) { if (src.length == 16) { System.arraycopy(src, 0, mBackingArray, 0, mBackingArray.length); } else { throw new IllegalArgumentException("Src array must be of length 16"); } } /** * Gets the value at the matrix's row and column. * * @param row An integer from 0 to 3 indicating the row of the value to get * @param col An integer from 0 to 3 indicating the column of the value to get */ @FlaggedApi(Flags.FLAG_MATRIX_44) public float get(@IntRange(from = 0, to = 3) int row, @IntRange(from = 0, to = 3) int col) { if (row >= 0 && row < 4 && col >= 0 && col < 4) { return mBackingArray[row * 4 + col]; } throw new IllegalArgumentException("invalid row and column values"); } /** * Sets the value at the matrix's row and column to the provided value. * * @param row An integer from 0 to 3 indicating the row of the value to change * @param col An integer from 0 to 3 indicating the column of the value to change * @param val The value the element at the specified index will be set to */ @FlaggedApi(Flags.FLAG_MATRIX_44) public void set(@IntRange(from = 0, to = 3) int row, @IntRange(from = 0, to = 3) int col, float val) { if (row >= 0 && row < 4 && col >= 0 && col < 4) { mBackingArray[row * 4 + col] = val; } else { throw new IllegalArgumentException("invalid row and column values"); } } /** * Sets the Matrix44 to the identity matrix. */ @FlaggedApi(Flags.FLAG_MATRIX_44) public void reset() { for (int i = 0; i < mBackingArray.length; i++) { mBackingArray[i] = (i % 4 == i / 4) ? 1.0f : 0.0f; } } /** * Inverts the Matrix44, then return true if successful, false if unable to invert. * * @return {@code true} on success, {@code false} otherwise */ @FlaggedApi(Flags.FLAG_MATRIX_44) public boolean invert() { float a00 = mBackingArray[0]; float a01 = mBackingArray[1]; float a02 = mBackingArray[2]; float a03 = mBackingArray[3]; float a10 = mBackingArray[4]; float a11 = mBackingArray[5]; float a12 = mBackingArray[6]; float a13 = mBackingArray[7]; float a20 = mBackingArray[8]; float a21 = mBackingArray[9]; float a22 = mBackingArray[10]; float a23 = mBackingArray[11]; float a30 = mBackingArray[12]; float a31 = mBackingArray[13]; float a32 = mBackingArray[14]; float a33 = mBackingArray[15]; float b00 = a00 * a11 - a01 * a10; float b01 = a00 * a12 - a02 * a10; float b02 = a00 * a13 - a03 * a10; float b03 = a01 * a12 - a02 * a11; float b04 = a01 * a13 - a03 * a11; float b05 = a02 * a13 - a03 * a12; float b06 = a20 * a31 - a21 * a30; float b07 = a20 * a32 - a22 * a30; float b08 = a20 * a33 - a23 * a30; float b09 = a21 * a32 - a22 * a31; float b10 = a21 * a33 - a23 * a31; float b11 = a22 * a33 - a23 * a32; float det = (b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06); if (det == 0.0f) { return false; } float invDet = 1.0f / det; mBackingArray[0] = ((a11 * b11 - a12 * b10 + a13 * b09) * invDet); mBackingArray[1] = ((-a01 * b11 + a02 * b10 - a03 * b09) * invDet); mBackingArray[2] = ((a31 * b05 - a32 * b04 + a33 * b03) * invDet); mBackingArray[3] = ((-a21 * b05 + a22 * b04 - a23 * b03) * invDet); mBackingArray[4] = ((-a10 * b11 + a12 * b08 - a13 * b07) * invDet); mBackingArray[5] = ((a00 * b11 - a02 * b08 + a03 * b07) * invDet); mBackingArray[6] = ((-a30 * b05 + a32 * b02 - a33 * b01) * invDet); mBackingArray[7] = ((a20 * b05 - a22 * b02 + a23 * b01) * invDet); mBackingArray[8] = ((a10 * b10 - a11 * b08 + a13 * b06) * invDet); mBackingArray[9] = ((-a00 * b10 + a01 * b08 - a03 * b06) * invDet); mBackingArray[10] = ((a30 * b04 - a31 * b02 + a33 * b00) * invDet); mBackingArray[11] = ((-a20 * b04 + a21 * b02 - a23 * b00) * invDet); mBackingArray[12] = ((-a10 * b09 + a11 * b07 - a12 * b06) * invDet); mBackingArray[13] = ((a00 * b09 - a01 * b07 + a02 * b06) * invDet); mBackingArray[14] = ((-a30 * b03 + a31 * b01 - a32 * b00) * invDet); mBackingArray[15] = ((a20 * b03 - a21 * b01 + a22 * b00) * invDet); return true; } /** * Returns true if Matrix44 is equal to identity matrix. */ @FlaggedApi(Flags.FLAG_MATRIX_44) public boolean isIdentity() { for (int i = 0; i < mBackingArray.length; i++) { float expected = (i % 4 == i / 4) ? 1.0f : 0.0f; if (expected != mBackingArray[i]) return false; } return true; } @FlaggedApi(Flags.FLAG_MATRIX_44) private static float dot(Matrix44 a, Matrix44 b, int row, int col) { return (a.get(row, 0) * b.get(0, col)) + (a.get(row, 1) * b.get(1, col)) + (a.get(row, 2) * b.get(2, col)) + (a.get(row, 3) * b.get(3, col)); } @FlaggedApi(Flags.FLAG_MATRIX_44) private static float dot(float r0, float r1, float r2, float r3, float c0, float c1, float c2, float c3) { return (r0 * c0) + (r1 * c1) + (r2 * c2) + (r3 * c3); } /** * Multiplies (x, y, z, w) vector by the Matrix44, then returns the new (x, y, z, w). Users * should set {@code w} to 1 to indicate the coordinates are normalized. * * @return An array of length 4 that represents the x, y, z, w (where w is perspective) value * after multiplying x, y, z, 1 by the matrix */ @FlaggedApi(Flags.FLAG_MATRIX_44) public @NonNull float[] map(float x, float y, float z, float w) { float[] dst = new float[4]; this.map(x, y, z, w, dst); return dst; } /** * Multiplies (x, y, z, w) vector by the Matrix44, then returns the new (x, y, z, w). Users * should set {@code w} to 1 to indicate the coordinates are normalized. */ @FlaggedApi(Flags.FLAG_MATRIX_44) public void map(float x, float y, float z, float w, @NonNull float[] dst) { if (dst.length != 4) { throw new IllegalArgumentException("Dst array must be of length 4"); } dst[0] = x * mBackingArray[0] + y * mBackingArray[1] + z * mBackingArray[2] + w * mBackingArray[3]; dst[1] = x * mBackingArray[4] + y * mBackingArray[5] + z * mBackingArray[6] + w * mBackingArray[7]; dst[2] = x * mBackingArray[8] + y * mBackingArray[9] + z * mBackingArray[10] + w * mBackingArray[11]; dst[3] = x * mBackingArray[12] + y * mBackingArray[13] + z * mBackingArray[14] + w * mBackingArray[15]; } /** * Multiplies `this` matrix (A) and provided Matrix (B) in the order of A * B. * The result is saved in `this` Matrix. * * @param b The second Matrix in the concatenation operation * @return A reference to this Matrix, which can be used to chain Matrix operations */ @FlaggedApi(Flags.FLAG_MATRIX_44) public @NonNull Matrix44 concat(@NonNull Matrix44 b) { float val00 = dot(this, b, 0, 0); float val01 = dot(this, b, 0, 1); float val02 = dot(this, b, 0, 2); float val03 = dot(this, b, 0, 3); float val10 = dot(this, b, 1, 0); float val11 = dot(this, b, 1, 1); float val12 = dot(this, b, 1, 2); float val13 = dot(this, b, 1, 3); float val20 = dot(this, b, 2, 0); float val21 = dot(this, b, 2, 1); float val22 = dot(this, b, 2, 2); float val23 = dot(this, b, 2, 3); float val30 = dot(this, b, 3, 0); float val31 = dot(this, b, 3, 1); float val32 = dot(this, b, 3, 2); float val33 = dot(this, b, 3, 3); mBackingArray[0] = val00; mBackingArray[1] = val01; mBackingArray[2] = val02; mBackingArray[3] = val03; mBackingArray[4] = val10; mBackingArray[5] = val11; mBackingArray[6] = val12; mBackingArray[7] = val13; mBackingArray[8] = val20; mBackingArray[9] = val21; mBackingArray[10] = val22; mBackingArray[11] = val23; mBackingArray[12] = val30; mBackingArray[13] = val31; mBackingArray[14] = val32; mBackingArray[15] = val33; return this; } /** * Applies a rotation around a given axis, then returns self. * {@code x}, {@code y}, {@code z} represent the axis by which to rotate around. * For example, pass in {@code 1, 0, 0} to rotate around the x-axis. * The axis provided will be normalized. * * @param deg Amount in degrees to rotate the matrix about the x-axis * @param xComp X component of the rotation axis * @param yComp Y component of the rotation axis * @param zComp Z component of the rotation axis * @return A reference to this Matrix, which can be used to chain Matrix operations */ @FlaggedApi(Flags.FLAG_MATRIX_44) public @NonNull Matrix44 rotate(float deg, float xComp, float yComp, float zComp) { float sum = xComp + yComp + zComp; float x = xComp / sum; float y = yComp / sum; float z = zComp / sum; float c = (float) Math.cos(deg * Math.PI / 180.0f); float s = (float) Math.sin(deg * Math.PI / 180.0f); float t = 1 - c; float rotVals00 = t * x * x + c; float rotVals01 = t * x * y - s * z; float rotVals02 = t * x * z + s * y; float rotVals10 = t * x * y + s * z; float rotVals11 = t * y * y + c; float rotVals12 = t * y * z - s * x; float rotVals20 = t * x * z - s * y; float rotVals21 = t * y * z + s * x; float rotVals22 = t * z * z + c; float v00 = dot(mBackingArray[0], mBackingArray[1], mBackingArray[2], mBackingArray[3], rotVals00, rotVals10, rotVals20, 0); float v01 = dot(mBackingArray[0], mBackingArray[1], mBackingArray[2], mBackingArray[3], rotVals01, rotVals11, rotVals21, 0); float v02 = dot(mBackingArray[0], mBackingArray[1], mBackingArray[2], mBackingArray[3], rotVals02, rotVals12, rotVals22, 0); float v03 = dot(mBackingArray[0], mBackingArray[1], mBackingArray[2], mBackingArray[3], 0, 0, 0, 1); float v10 = dot(mBackingArray[4], mBackingArray[5], mBackingArray[6], mBackingArray[7], rotVals00, rotVals10, rotVals20, 0); float v11 = dot(mBackingArray[4], mBackingArray[5], mBackingArray[6], mBackingArray[7], rotVals01, rotVals11, rotVals21, 0); float v12 = dot(mBackingArray[4], mBackingArray[5], mBackingArray[6], mBackingArray[7], rotVals02, rotVals12, rotVals22, 0); float v13 = dot(mBackingArray[4], mBackingArray[5], mBackingArray[6], mBackingArray[7], 0, 0, 0, 1); float v20 = dot(mBackingArray[8], mBackingArray[9], mBackingArray[10], mBackingArray[11], rotVals00, rotVals10, rotVals20, 0); float v21 = dot(mBackingArray[8], mBackingArray[9], mBackingArray[10], mBackingArray[11], rotVals01, rotVals11, rotVals21, 0); float v22 = dot(mBackingArray[8], mBackingArray[9], mBackingArray[10], mBackingArray[11], rotVals02, rotVals12, rotVals22, 0); float v23 = dot(mBackingArray[8], mBackingArray[9], mBackingArray[10], mBackingArray[11], 0, 0, 0, 1); float v30 = dot(mBackingArray[12], mBackingArray[13], mBackingArray[14], mBackingArray[15], rotVals00, rotVals10, rotVals20, 0); float v31 = dot(mBackingArray[12], mBackingArray[13], mBackingArray[14], mBackingArray[15], rotVals01, rotVals11, rotVals21, 0); float v32 = dot(mBackingArray[12], mBackingArray[13], mBackingArray[14], mBackingArray[15], rotVals02, rotVals12, rotVals22, 0); float v33 = dot(mBackingArray[12], mBackingArray[13], mBackingArray[14], mBackingArray[15], 0, 0, 0, 1); mBackingArray[0] = v00; mBackingArray[1] = v01; mBackingArray[2] = v02; mBackingArray[3] = v03; mBackingArray[4] = v10; mBackingArray[5] = v11; mBackingArray[6] = v12; mBackingArray[7] = v13; mBackingArray[8] = v20; mBackingArray[9] = v21; mBackingArray[10] = v22; mBackingArray[11] = v23; mBackingArray[12] = v30; mBackingArray[13] = v31; mBackingArray[14] = v32; mBackingArray[15] = v33; return this; } /** * Applies scaling factors to `this` Matrix44, then returns self. Pass 1s for no change. * * @param x Scaling factor for the x-axis * @param y Scaling factor for the y-axis * @param z Scaling factor for the z-axis * @return A reference to this Matrix, which can be used to chain Matrix operations */ @FlaggedApi(Flags.FLAG_MATRIX_44) public @NonNull Matrix44 scale(float x, float y, float z) { mBackingArray[0] *= x; mBackingArray[4] *= x; mBackingArray[8] *= x; mBackingArray[12] *= x; mBackingArray[1] *= y; mBackingArray[5] *= y; mBackingArray[9] *= y; mBackingArray[13] *= y; mBackingArray[2] *= z; mBackingArray[6] *= z; mBackingArray[10] *= z; mBackingArray[14] *= z; return this; } /** * Applies a translation to `this` Matrix44, then returns self. * * @param x Translation for the x-axis * @param y Translation for the y-axis * @param z Translation for the z-axis * @return A reference to this Matrix, which can be used to chain Matrix operations */ @FlaggedApi(Flags.FLAG_MATRIX_44) public @NonNull Matrix44 translate(float x, float y, float z) { float newX = x * mBackingArray[0] + y * mBackingArray[1] + z * mBackingArray[2] + mBackingArray[3]; float newY = x * mBackingArray[4] + y * mBackingArray[5] + z * mBackingArray[6] + mBackingArray[7]; float newZ = x * mBackingArray[8] + y * mBackingArray[9] + z * mBackingArray[10] + mBackingArray[11]; float newW = x * mBackingArray[12] + y * mBackingArray[13] + z * mBackingArray[14] + mBackingArray[15]; mBackingArray[3] = newX; mBackingArray[7] = newY; mBackingArray[11] = newZ; mBackingArray[15] = newW; return this; } @Override public String toString() { return String.format(""" | %f %f %f %f | | %f %f %f %f | | %f %f %f %f | | %f %f %f %f | """, mBackingArray[0], mBackingArray[1], mBackingArray[2], mBackingArray[3], mBackingArray[4], mBackingArray[5], mBackingArray[6], mBackingArray[7], mBackingArray[8], mBackingArray[9], mBackingArray[10], mBackingArray[11], mBackingArray[12], mBackingArray[13], mBackingArray[14], mBackingArray[15]); } @Override public boolean equals(Object obj) { if (obj instanceof Matrix44) { return Arrays.equals(mBackingArray, ((Matrix44) obj).mBackingArray); } return false; } @Override public int hashCode() { return (int) mBackingArray[0] + (int) mBackingArray[1] + (int) mBackingArray[2] + (int) mBackingArray[3] + (int) mBackingArray[4] + (int) mBackingArray[5] + (int) mBackingArray[6] + (int) mBackingArray[7] + (int) mBackingArray[8] + (int) mBackingArray[9] + (int) mBackingArray[10] + (int) mBackingArray[11] + (int) mBackingArray[12] + (int) mBackingArray[13] + (int) mBackingArray[14] + (int) mBackingArray[15]; } }