1 前言
纹理贴图 中介绍了将矩形图片贴到矩形模型上，本文将介绍：在不裁剪图片的情况下，将正方形的图片贴到圆形模型上。
思考：实数区间 [0, 1] 与 [0, 2] 的元素可以建立一一映射关系么？答案是肯定的，如：y=2x、y=2x2、y=2*ex/e^2、y=2ln(x+1)/ln2、y=2sin(π/2*x) 等等，其中 x∈[0, 1]，y∈[0, 2]。
同理，在二维平面上，也可以构造一个函数，使得正方形上的点与圆形上的点一一对应。映射的构建如下图：
原图如下：
映射如下：
读者如果对 OpenGL ES 不太熟悉，请回顾以下内容：
本文完整代码资源见→【OpenGL ES】正方形图片贴到圆形上
项目目录如下：
2 案例
MainActivity.java
package com.zhyan8.squaretocircle.activity;
import android.opengl.GLSurfaceView;
import android.os.Bundle;
import androidx.appcompat.app.AppCompatActivity;
import com.zhyan8.squaretocircle.opengl.MyGLSurfaceView;
import com.zhyan8.squaretocircle.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(this));
}
@Override
protected void onResume() {
super.onResume();
mGlSurfaceView.onResume();
}
@Override
protected void onPause() {
super.onPause();
mGlSurfaceView.onPause();
}
}
MyGLSurfaceView.java
package com.zhyan8.squaretocircle.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.squaretocircle.opengl;
import android.content.Context;
import android.opengl.GLES30;
import android.opengl.GLSurfaceView;
import com.zhyan8.squaretocircle.model.Model;
import javax.microedition.khronos.egl.EGLConfig;
import javax.microedition.khronos.opengles.GL10;
public class MyRender implements GLSurfaceView.Renderer {
private Context mContext;
private Model mModel;
private int mProgramId;
public MyRender(Context context) {
mContext = context;
mModel = new Model();
}
@Override
public void onSurfaceCreated(GL10 gl, EGLConfig eglConfig) {
//设置背景颜色
GLES30.glClearColor(0.0f, 0.0f, 0.0f, 1.0f);
//创建程序id
mProgramId = mModel.onModelCreate(mContext.getResources());
GLES30.glUseProgram(mProgramId);
}
@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);
//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.squaretocircle.model;
import android.content.res.Resources;
import android.graphics.Point;
import android.opengl.GLES30;
import com.zhyan8.squaretocircle.R;
import com.zhyan8.squaretocircle.utils.ArraysUtils;
import com.zhyan8.squaretocircle.utils.ShaderUtils;
import com.zhyan8.squaretocircle.utils.TextureUtils;
import java.nio.FloatBuffer;
public class Model {
private static final int ROW_NUM = 60; // 纹理行数
private static final int COL_NUM = 60; // 纹理列数
private static final float ROW_WIDTH = 1.0f / ROW_NUM; // 每行宽度
private static final float COL_WIDTH = 1.0f / COL_NUM; // 每列宽度
private static final float SCALE = 1.0f; // 模型缩放系数
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 MyTransform mTransform = new MyTransform();
private float[][] mTextures;
private float[][] mVertices;
private FloatBuffer[] mTexturesBuffers;
private FloatBuffer[] mVerticesBuffers;
private int mTextureId;
private int mProgramId;
private int mPointNumPerRow;
public Model() {
mPointNumPerRow = (COL_NUM + 1) * 2;
mTextures = new float[ROW_NUM][mPointNumPerRow * TEXTURE_DIMENSION];
mVertices = new float[ROW_NUM][mPointNumPerRow * VERTEX_DIMENSION];
mTexturesBuffers = new FloatBuffer[ROW_NUM];
mVerticesBuffers = new FloatBuffer[ROW_NUM];
}
// 模型创建
public int onModelCreate(Resources resources) {
getTexture();
getVertex();
for (int i = 0; i < ROW_NUM; i++) {
mTexturesBuffers[i] = ArraysUtils.getFloatBuffer(mTextures[i]);
mVerticesBuffers[i] = ArraysUtils.getFloatBuffer(mVertices[i]);
}
mProgramId = ShaderUtils.createProgram(resources, R.raw.vertex_shader, R.raw.fragment_shader);
Point bitmapSize = new Point();
mTextureId = TextureUtils.loadTexture(resources, R.raw.zzz, bitmapSize);
mTransform.onTransformCreate(mProgramId, bitmapSize);
return 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() {
mTransform.onTransformExecute();
for (int i = 0; i < ROW_NUM; i++) { // 一行一行绘制纹理
//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, mPointNumPerRow);
// GLES30.glDrawArrays(GLES30.GL_LINE_STRIP, 0, mPointNumPerRow);
}
}
// 计算纹理坐标
private void getTexture() {
for (int i = 0; i < ROW_NUM; i++) {
int index = 0;
float y1 = i * ROW_WIDTH;
float y2 = y1 + ROW_WIDTH;
float x = 0;
for (int j = 0; j <= COL_NUM; j++) {
mTextures[i][index++] = x;
mTextures[i][index++] = y1;
mTextures[i][index++] = x;
mTextures[i][index++] = y2;
x += COL_WIDTH;
}
}
}
// 计算顶点坐标
private void getVertex() {
for (int i = 0; i < ROW_NUM; i++) {
int index = 0;
for (int j = 0; j < mTextures[i].length; j += TEXTURE_DIMENSION) {
float[] pos = getPosInWorldAxis(mTextures[i][j], mTextures[i][j + 1]);
textureVertexMapping(pos);
mVertices[i][index++] = pos[0] * SCALE;
mVertices[i][index++] = pos[1] * SCALE;
mVertices[i][index++] = pos[2] * SCALE;
}
}
}
// 纹理坐标映射到顶点坐标
private void textureVertexMapping(float[] pos) {
float x = Math.abs(pos[0]);
float y = Math.abs(pos[1]);
double norm = Math.sqrt(x * x + y * y);
if (norm < EPSILON) {
return;
}
double normX = pos[0] / norm; // 归一化坐标
double normY = pos[1] / norm; // 归一化坐标
double rate = x > y ? y / x : x / y; // 短边与长边的比率
double dist = Math.sqrt(1 + rate * rate); // 圆心到正方形边上的距离
double factor = norm / dist; // 相对位置缩放因子
// double adjustNorm = adjustDist(norm);
// double adjustDist = adjustDist(dist);
// double factor = adjustNorm / adjustDist; // 相对位置缩放因子
pos[0] = (float) (normX * fun(factor));
pos[1] = (float) (normY * fun(factor));
}
// 调整距离
private double adjustDist(double dist) {
if (dist < 1) return dist;
double rest = dist - 1;
double more = rest / 2;
return 1 + more;
}
// 因子变换函数
private double fun(double x) {
return x;
// return Math.sqrt(x);
// return Math.pow(x, 0.3);
// return Math.log(x + 1) / Math.log(2);
// return Math.log10(x + 1) / Math.log10(2);
// return Math.sin(Math.PI / 2 * x);
}
//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] = 0f;
return pos;
}
}
MyTransform.java
package com.zhyan8.squaretocircle.model;
import android.graphics.Point;
import android.opengl.GLES30;
import android.opengl.Matrix;
public class MyTransform {
private int mProgramId;
private Point mBitmapSize;
private Point mViewSize;
private int mMvpMatrixHandle;
private float[] mMvpMatrix = new float[16];
public void onTransformCreate(int programId, Point bitmapSize) {
mProgramId = programId;
mBitmapSize = bitmapSize;
mMvpMatrixHandle = GLES30.glGetUniformLocation(mProgramId, "mvpMatrix");
}
public void onTransformChange(int width, int height) {
mViewSize = new Point(width, height);
}
//调整图片宽高适配屏幕尺寸
public void onTransformExecute() {
int mapWidth = mBitmapSize.x;
int mapHeight = mBitmapSize.y;
float mapRatio = mapWidth / (float) mapHeight;
float ratio = mViewSize.x / (float) mViewSize.y;
float w = 1.0f;
float h = 1.0f;
if (mapRatio > ratio) { //宽度最大，高度适配
h = mapRatio / ratio;
} else { //高度最大，宽度适配
w = ratio / mapRatio;
}
Matrix.orthoM(mMvpMatrix, 0, -w, w, -h, h,-1, 1);
GLES30.glUniformMatrix4fv(mMvpMatrixHandle, 1, false, mMvpMatrix, 0);
}
}
ShaderUtils.java
package com.zhyan8.squaretocircle.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.squaretocircle.utils;
import android.content.res.Resources;
import android.graphics.Bitmap;
import android.graphics.BitmapFactory;
import android.graphics.Point;
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, Point bitmapSize) {
BitmapFactory.Options options = new BitmapFactory.Options();
options.inScaled = false;
Bitmap bitmap = BitmapFactory.decodeResource(resources, resourceId, options);
bitmapSize.set(bitmap.getWidth(), bitmap.getHeight());
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.squaretocircle.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;
}
顶点着色器的作用：进行矩阵变换位置、根据光照公式计算顶点颜⾊、⽣成 / 变换纹理坐标，并且把位置和纹理坐标发送到片元着色器。
顶点着色器中，如果没有指定默认精度，则 int 和 float 的默认精度都为 highp。
fragment_shader.glsl
#version 300 es
precision mediump float;
uniform sampler2D uTextureUnit;
in vec2 vTexCoord;
out vec4 fragColor;
void main() {
fragColor = texture(uTextureUnit,vTexCoord);
}
片元着色器的作用：处理经光栅化阶段生成的每个片元，计算每个像素的颜色和透明度。
在片元着色器中，浮点值没有默认的精度值，每个着色器必须声明一个默认的 float 精度。
3 运行效果
1）因子变换函数：y=x
2）因子变换函数：y=sqrt(x)
3）因子变换函数：y=log10(1+x)/log10(2)
4）因子变换函数：y=sin(πx/2)
5）因子变换函数：y=x，对距离进行调整
鉴于以上图片头发都鼓起一个大包，对距离进行调整，如下：
double adjustNorm = adjustDist(norm);
double adjustDist = adjustDist(dist);
double factor = adjustNorm / adjustDist; // 相对位置缩放因子
// 调整距离
private double adjustDist(double dist) {
if (dist < 1) return dist;
double rest = dist - 1;
double more = rest / 2;
return 1 + more;
}
效果如下：
虽然头发也有个小包，但比前面4种方案小了很多。
声明：本文转自【OpenGL ES】正方形图片贴到圆形上
