參考資料：

• 正射投影：https://www.cnblogs.com/hackpig/p/5790379.html
• 透射投影：https://blog.csdn.net/linuxheik/article/details/78969526

坐標變換

在頂點著色器定義一個頂點變換矩陣，與輸入的頂點向量相乘，得到新的頂點位置

#version 330 core layout (location = 0) in vec3 aPos; layout (location = 1) in vec2 aTexCoord;out vec2 TexCoord;uniform mat4 transform;void main() {gl_Position = transform * vec4(aPos, 1.0f);TexCoord = vec2(aTexCoord.x, 1.0 - aTexCoord.y); }

其中uniform mat4 transform 就是一個全局變換矩陣，它可以用glm庫函數來賦值：

// create transformationsglm::mat4 transform = glm::mat4(1.0f); // make sure to initialize matrix to identity matrix firsttransform = glm::translate(transform, glm::vec3(0.5f, -0.5f, 0.0f));transform = glm::rotate(transform, (float)glfwGetTime(), glm::vec3(0.0f, 0.0f, 1.0f));// get matrix's uniform location and set matrixourShader.use();unsigned int transformLoc = glGetUniformLocation(ourShader.ID, "transform");glUniformMatrix4fv(transformLoc, 1, GL_FALSE, glm::value_ptr(transform));

坐標空間

OpenGL一共有5個坐標系，通過5個坐標系的變換，將一個物體的局部坐標下的形狀最終變換到屏幕坐標下。這幾個坐標系都有明確的物理含義：

其中需要注意以下裁剪坐標：
裁剪坐標有兩種方式正射投影和透視投影，透視投影能模仿人眼看遠方的效果但是正射投影不能。正射投影將一個長方體裁剪區映射到設備坐標，但是透視投影將一個視椎體區域映射到設備坐標。
放兩張圖，具體原理可以看上面參考資料：
正視投影

透視投影

坐標空間變換代碼：

#version 330 core layout (location = 0) in vec3 aPos; layout (location = 1) in vec2 aTexCoord;out vec2 TexCoord;uniform mat4 model; uniform mat4 view; uniform mat4 projection;void main() {gl_Position = projection * view * model * vec4(aPos, 1.0f);TexCoord = vec2(aTexCoord.x, aTexCoord.y); }``` /注/意矩陣相乘的順序```cpp glm::mat4 model = glm::mat4(1.0f); // make sure to initialize matrix to identity matrix firstglm::mat4 view = glm::mat4(1.0f);glm::mat4 projection = glm::mat4(1.0f);model = glm::rotate(model, (float)glfwGetTime(), glm::vec3(0.5f, 1.0f, 0.0f));view = glm::translate(view, glm::vec3(0.0f, 0.0f, -3.0f));projection = glm::perspective(glm::radians(45.0f), (float)SCR_WIDTH / (float)SCR_HEIGHT, 0.1f, 100.0f);// retrieve the matrix uniform locationsunsigned int modelLoc = glGetUniformLocation(ourShader.ID, "model");unsigned int viewLoc = glGetUniformLocation(ourShader.ID, "view");// pass them to the shaders (3 different ways)glUniformMatrix4fv(modelLoc, 1, GL_FALSE, glm::value_ptr(model));glUniformMatrix4fv(viewLoc, 1, GL_FALSE, &view[0][0]);// note: currently we set the projection matrix each frame, but since the projection matrix rarely changes it's often best practice to set it outside the main loop only once.ourShader.setMat4("projection", projection);

其它

通過使用不同的空間坐標系，在屏幕上展現多個同一張圖像

glBindVertexArray(VAO); for(unsigned int i = 0; i < 10; i++) {glm::mat4 model;model = glm::translate(model, cubePositions[i]);float angle = 20.0f * i; model = glm::rotate(model, glm::radians(angle), glm::vec3(1.0f, 0.3f, 0.5f));ourShader.setMat4("model", model);glDrawArrays(GL_TRIANGLES, 0, 36); }

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