【OpenGL ES】凸镜贴图

1 前言

正方形图片贴到圆形上中将正方形图片上的纹理映射到圆形模型上，同理，也可以将圆形上的纹理映射到凸镜的球形曲面上。如下图，最左边的竖条是原图片的截面（纹理坐标），最右边的竖条是变换后的顶点模型截面（顶点坐标）。

原图如下：

读者如果对 OpenGL ES 不太熟悉，请回顾以下内容：

Unity3D Shader 版本实现见→半球卷屏特效。

本文完整代码资源见→【OpenGL ES】凸镜贴图

项目目录如下：

2 案例

MainActivity.java

package com.zhyan8.convexMirror.activity;

import android.opengl.GLSurfaceView;
import android.os.Bundle;
import androidx.appcompat.app.AppCompatActivity;
import com.zhyan8.convexMirror.opengl.MyGLSurfaceView;
import com.zhyan8.convexMirror.opengl.MyRender;

public class MainActivity extends AppCompatActivity {
    private GLSurfaceView mGlSurfaceView;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        mGlSurfaceView = new MyGLSurfaceView(this);
        setContentView(mGlSurfaceView);
        mGlSurfaceView.setRenderer(new MyRender(getResources()));
    }

    @Override
    protected void onResume() {
        super.onResume();
        mGlSurfaceView.onResume();
    }

    @Override
    protected void onPause() {
        super.onPause();
        mGlSurfaceView.onPause();
    }
}

MyGLSurfaceView.java

package com.zhyan8.convexMirror.opengl;

import android.content.Context;
import android.opengl.GLSurfaceView;
import android.util.AttributeSet;

public class MyGLSurfaceView extends GLSurfaceView {
    public MyGLSurfaceView(Context context) {
        super(context);
        setEGLContextClientVersion(3);
    }

    public MyGLSurfaceView(Context context, AttributeSet attrs) {
        super(context, attrs);
        setEGLContextClientVersion(3);
    }
}

MyRender.java

package com.zhyan8.convexMirror.opengl;

import android.content.res.Resources;
import android.opengl.GLES30;
import android.opengl.GLSurfaceView;
import com.zhyan8.convexMirror.model.Model;
import javax.microedition.khronos.egl.EGLConfig;
import javax.microedition.khronos.opengles.GL10;

public class MyRender implements GLSurfaceView.Renderer {
    private Model mModel;

    public MyRender(Resources resources) {
        mModel = new Model(resources);
    }

    @Override
    public void onSurfaceCreated(GL10 gl, EGLConfig eglConfig) {
        //设置背景颜色
        GLES30.glClearColor(0.0f, 0.0f, 0.0f, 1.0f);
        //启动深度测试
        gl.glEnable(GLES30.GL_DEPTH_TEST);
        mModel.onModelCreate();
    }

    @Override
    public void onSurfaceChanged(GL10 gl, int width, int height) {
        //设置视图窗口
        GLES30.glViewport(0, 0, width, height);
        mModel.onModelChange(width, height);
    }

    @Override
    public void onDrawFrame(GL10 gl) {
        //将颜色缓冲区设置为预设的颜色
        GLES30.glClear(GLES30.GL_COLOR_BUFFER_BIT | GLES30.GL_DEPTH_BUFFER_BIT);
        //启用顶点的数组句柄
        GLES30.glEnableVertexAttribArray(0);
        GLES30.glEnableVertexAttribArray(1);
        //绘制模型
        mModel.onModelDraw();
        //禁止顶点数组句柄
        GLES30.glDisableVertexAttribArray(0);
        GLES30.glDisableVertexAttribArray(1);
    }
}

Model.java

package com.zhyan8.convexMirror.model;

import android.content.res.Resources;
import android.opengl.GLES30;
import com.zhyan8.convexMirror.R;
import com.zhyan8.convexMirror.utils.ArraysUtils;
import com.zhyan8.convexMirror.utils.ShaderUtils;
import com.zhyan8.convexMirror.utils.TextureUtils;
import java.nio.FloatBuffer;

public class Model {
    private static final int RING_NUM = 30; // 环数
    private static final int RAW_NUM = 50; // 射线数
    private static final double CONE_SECTION_FAN_ANGLE = 170.0 / 180.0 * Math.PI; // 圆锥凸镜截面扇形弧度（180度为半球）
    private static final double RING_WIDTH = 1.0 / RING_NUM; // 环宽度
    private static final double RAW_GAP_ANGLE = 2 * Math.PI / RAW_NUM; // 两条射线间最小夹角
    private static final int TEXTURE_DIMENSION = 2; // 纹理坐标维度
    private static final int VERTEX_DIMENSION = 3; // 顶点坐标维度
    private static final double EPSILON = 0.00000000001; // epsilon，比较小的浮点常量
    private Resources mResources;
    private MyTransform mTransform;
    private float[][] mTextures;
    private float[][] mVertices;
    private FloatBuffer[] mTexturesBuffers;
    private FloatBuffer[] mVerticesBuffers;
    private int mTextureId;
    private int mProgramId;
    private int mPointNumPerRing;

    public Model(Resources resources) {
        mResources = resources;
        mPointNumPerRing = (RAW_NUM + 1) * 2;
        mTextures = new float[RING_NUM][mPointNumPerRing * TEXTURE_DIMENSION];
        mVertices = new float[RING_NUM][mPointNumPerRing * VERTEX_DIMENSION];
        mTexturesBuffers = new FloatBuffer[RING_NUM];
        mVerticesBuffers = new FloatBuffer[RING_NUM];
        mTransform = new MyTransform();
    }

    // 模型创建
    public void onModelCreate() {
        for (int i = 0; i < RING_NUM; i++) {
            getRingTexture(i);
            getRingVertex(i);
            mTexturesBuffers[i] = ArraysUtils.getFloatBuffer(mTextures[i]);
            mVerticesBuffers[i] = ArraysUtils.getFloatBuffer(mVertices[i]);
        }
        mProgramId = ShaderUtils.createProgram(mResources, R.raw.vertex_shader, R.raw.fragment_shader);
        mTextureId = TextureUtils.loadTexture(mResources, R.raw.zzz);
        mTransform.onTransformCreate(mProgramId);
    }

    // 模型参数变化
    public void onModelChange(int width, int height) {
        mTransform.onTransformChange(width, height);
    }

    // 模型绘制
    public void onModelDraw() {
        GLES30.glUseProgram(mProgramId);
        mTransform.onTransformExecute();
        for (int i = 0; i < RING_NUM; i++) { // 一环一环绘制纹理
            //准备顶点坐标和纹理坐标
            GLES30.glVertexAttribPointer(0, VERTEX_DIMENSION, GLES30.GL_FLOAT, false, 0, mVerticesBuffers[i]);
            GLES30.glVertexAttribPointer(1, TEXTURE_DIMENSION, GLES30.GL_FLOAT, false, 0, mTexturesBuffers[i]);
            //激活纹理
            GLES30.glActiveTexture(GLES30.GL_TEXTURE);
            //绑定纹理
            GLES30.glBindTexture(GLES30.GL_TEXTURE_2D, mTextureId);
            //绘制贴图
            GLES30.glDrawArrays(GLES30.GL_TRIANGLE_STRIP, 0, mPointNumPerRing);
//            GLES30.glDrawArrays(GLES30.GL_LINE_STRIP, 0, mPointNumPerRing);
        }
    }

    // 计算纹理坐标
    private void getRingTexture(int ring) {
        int rayNum = RAW_NUM + 1;
        double theta = 0;
        double radius1 = ring * RING_WIDTH / 2;
        double radius2 = (ring + 1) * RING_WIDTH / 2;
        int index = 0;
        for (int i = 0; i < rayNum; i++) {
            mTextures[ring][index++] = (float) (0.5 + radius1 * Math.cos(theta));
            mTextures[ring][index++] = (float) (0.5 - radius1 * Math.sin(theta));
            mTextures[ring][index++] = (float) (0.5 + radius2 * Math.cos(theta));
            mTextures[ring][index++] = (float) (0.5 - radius2 * Math.sin(theta));
            theta += RAW_GAP_ANGLE;
        }
    }

    // 计算顶点坐标
    private void getRingVertex(int ring) {
        int index = 0;
        for (int i = 0; i < mTextures[ring].length; i += TEXTURE_DIMENSION) {
            float[] pos = getPosInWorldAxis(mTextures[ring][i], mTextures[ring][i + 1]);
            textureVertexMapping(pos);
            mVertices[ring][index++] = pos[0];
            mVertices[ring][index++] = pos[1];
            mVertices[ring][index++] = pos[2];
        }
    }

    // 纹理坐标映射到顶点坐标
    private void textureVertexMapping(float[] pos) {
        double norm = Math.sqrt(pos[0] * pos[0] + pos[1] * pos[1]);
        double alpha = CONE_SECTION_FAN_ANGLE / 2;
        double beta = norm * alpha;
        if (norm > EPSILON) {
            double factor = Math.sin(beta) / Math.sin(alpha) / norm;
            pos[0] = (float) (pos[0] * factor);
            pos[1] = (float) (pos[1] * factor);
        }
        pos[2] = (float) ((Math.cos(beta) - Math.cos(alpha)) / Math.sin(alpha));
    }

    //纹理坐标转换为世界坐标
    private float[] getPosInWorldAxis(float x, float y) {
        float [] pos = new float[VERTEX_DIMENSION];
        pos[0] = x * 2 - 1;
        pos[1] = 1 - y * 2;
        pos[2] = 1f;
        return pos;
    }
}

MyTransform.java

package com.zhyan8.convexMirror.model;

import android.opengl.GLES30;
import android.opengl.Matrix;

public class MyTransform {
    private static final float SCALE_RATE = 1.0f; // 模型缩放系数
    private int mProgramId;
    private float mRatio;
    private int mRotateAgree = 0;
    private int mMvpMatrixHandle;
    private float[] mModelMatrix;
    private float[] mViewMatrix;
    private float[] mProjectionMatrix;
    private float[] mMvpMatrix;

    // 变换创建
    public void onTransformCreate(int programId) {
        mProgramId = programId;
        mMvpMatrixHandle = GLES30.glGetUniformLocation(mProgramId, "mvpMatrix");
        mViewMatrix = getIdentityMatrix(16, 0);
        mMvpMatrix = getIdentityMatrix(16, 0);
        Matrix.setLookAtM(mViewMatrix, 0, 0, 0, 6, 0, 0, 0, 0, 1, 0);
    }

    // 变换参数变换
    public void onTransformChange(int width, int height) {
        mRatio = 1.0f * width / height;
        mProjectionMatrix = getIdentityMatrix(16, 0);
        Matrix.frustumM(mProjectionMatrix, 0, -mRatio, mRatio, -1, 1, 3, 20);
    }

    // 变换执行
    public void onTransformExecute() {
        mModelMatrix = getIdentityMatrix(16, 0);
        mRotateAgree = (mRotateAgree + 1) % 360;
        Matrix.rotateM(mModelMatrix, 0, mRotateAgree, -1, -1, 1);
        Matrix.scaleM(mModelMatrix, 0, SCALE_RATE, SCALE_RATE, SCALE_RATE);
        //计算MVP变换矩阵: mvpMatrix = projectionMatrix * viewMatrix * modelMatrix
        float[] tempMatrix = new float[16];
        Matrix.multiplyMM(tempMatrix, 0, mViewMatrix, 0, mModelMatrix, 0);
        Matrix.multiplyMM(mMvpMatrix, 0, mProjectionMatrix, 0, tempMatrix, 0);
        GLES30.glUniformMatrix4fv(mMvpMatrixHandle, 1, false, mMvpMatrix, 0);
    }

    private float[] getIdentityMatrix(int size, int offset) {
        float[] matrix = new float[size];
        Matrix.setIdentityM(matrix, offset);
        return matrix;
    }
}

ShaderUtils.java

package com.zhyan8.convexMirror.utils;

import android.content.res.Resources;
import android.opengl.GLES30;
import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;

public class ShaderUtils {
    //创建程序id
    public static int createProgram(Resources resources, int vertexShaderResId, int fragmentShaderResId) {
        final int vertexShaderId = compileShader(resources, GLES30.GL_VERTEX_SHADER, vertexShaderResId);
        final int fragmentShaderId = compileShader(resources, GLES30.GL_FRAGMENT_SHADER, fragmentShaderResId);
        return linkProgram(vertexShaderId, fragmentShaderId);
    }

    //通过外部资源编译着色器
    private static int compileShader(Resources resources, int type, int shaderId){
        String shaderCode = readShaderFromResource(resources, shaderId);
        return compileShader(type, shaderCode);
    }

    //通过代码片段编译着色器
    private static int compileShader(int type, String shaderCode){
        int shader = GLES30.glCreateShader(type);
        GLES30.glShaderSource(shader, shaderCode);
        GLES30.glCompileShader(shader);
        return shader;
    }

    //链接到着色器
    private static int linkProgram(int vertexShaderId, int fragmentShaderId) {
        final int programId = GLES30.glCreateProgram();
        //将顶点着色器加入到程序
        GLES30.glAttachShader(programId, vertexShaderId);
        //将片元着色器加入到程序
        GLES30.glAttachShader(programId, fragmentShaderId);
        //链接着色器程序
        GLES30.glLinkProgram(programId);
        return programId;
    }

    //从shader文件读出字符串
    private static String readShaderFromResource(Resources resources, int shaderId) {
        InputStream is = resources.openRawResource(shaderId);
        BufferedReader br = new BufferedReader(new InputStreamReader(is));
        String line;
        StringBuilder sb = new StringBuilder();
        try {
            while ((line = br.readLine()) != null) {
                sb.append(line);
                sb.append("\n");
            }
            br.close();
        } catch (Exception e) {
            e.printStackTrace();
        }
        return sb.toString();
    }
}

TextureUtils.java

package com.zhyan8.convexMirror.utils;

import android.content.res.Resources;
import android.graphics.Bitmap;
import android.graphics.BitmapFactory;
import android.opengl.GLES30;
import android.opengl.GLUtils;

public class TextureUtils {
    //加载纹理贴图
    public static int loadTexture(Resources resources, int resourceId) {
        BitmapFactory.Options options = new BitmapFactory.Options();
        options.inScaled = false;
        Bitmap bitmap = BitmapFactory.decodeResource(resources, resourceId, options);
        final int[] textureIds = new int[1];
        // 生成纹理id
        GLES30.glGenTextures(1, textureIds, 0);
        // 绑定纹理到OpenGL
        GLES30.glBindTexture(GLES30.GL_TEXTURE_2D, textureIds[0]);
        GLES30.glTexParameteri(GLES30.GL_TEXTURE_2D, GLES30.GL_TEXTURE_MIN_FILTER, GLES30.GL_LINEAR_MIPMAP_LINEAR);
        GLES30.glTexParameteri(GLES30.GL_TEXTURE_2D, GLES30.GL_TEXTURE_MAG_FILTER, GLES30.GL_LINEAR);
        // 加载bitmap到纹理中
        GLUtils.texImage2D(GLES30.GL_TEXTURE_2D, 0, bitmap, 0);
        // 生成MIP贴图
        GLES30.glGenerateMipmap(GLES30.GL_TEXTURE_2D);
        // 取消绑定纹理
        GLES30.glBindTexture(GLES30.GL_TEXTURE_2D, 0);
        return textureIds[0];
    }
}

ArraysUtils.java

package com.zhyan8.convexMirror.utils;

import java.nio.ByteBuffer;
import java.nio.ByteOrder;
import java.nio.FloatBuffer;

public class ArraysUtils {
    public static FloatBuffer getFloatBuffer(float[] floatArr) {
        FloatBuffer fb = ByteBuffer.allocateDirect(floatArr.length * Float.BYTES)
            .order(ByteOrder.nativeOrder())
            .asFloatBuffer();
        fb.put(floatArr);
        fb.position(0);
        return fb;
    }
}

vertex_shader.glsl

#version 300 es
layout (location = 0) in vec4 vPosition;
layout (location = 1) in vec2 aTextureCoord;
uniform mat4 mvpMatrix;
out vec2 vTexCoord;
void main() {
     gl_Position  = mvpMatrix * vPosition;
     vTexCoord = aTextureCoord;
}

fragment_shader.glsl

#version 300 es
precision mediump float;
uniform sampler2D uTextureUnit;
in vec2 vTexCoord;
out vec4 fragColor;
void main() {
     fragColor = texture(uTextureUnit,vTexCoord);
}