OpenGL。将顶点乘以投影矩阵

Question

我正在尝试绘制一个模型，这就是我运行所做的，下面的代码像 2d 一样工作，尽管应该有一个透视图

Code # 1
mat4 Proj = glFrustum(left, right, bottom, top, zNear, zFar);
mat4 View = gluLookAt(position, direction, up);
mat4 World = mat4(1);
glBegin(GL_TRIANGLES);
for (auto& t : mesh)
{
    norm = Proj * View * World * vec4(t.norm, 0);
    dot1 = Proj * View * World * vec4(t.dot1, 1);
    dot2 = Proj * View * World * vec4(t.dot2, 1);
    dot3 = Proj * View * World * vec4(t.dot3, 1);
 
    glNormal3f(norm);
    glVertex3f(dot1.x, dot1.y, dot1.z);
    glVertex3f(dot2.x, dot2.y, dot3.z);
    glVertex3f(dot3.x, dot3.y, dot3.z);
}
glEnd();

于是透视图出现：

Code # 2
mat4 Proj = glFrustum(left, right, bottom, top, zNear, zFar);
mat4 View = gluLookAt(position, direction, up);
mat4 World = mat4(1);
glMatrixMode(GL_PROJECTION);
glLoadMatrix(Proj);
glBegin(GL_TRIANGLES);
for (auto& t : mesh)
{
    norm = View * World * vec4(t.norm, 0);
    dot1 = View * World * vec4(t.dot1, 1);
    dot2 = View * World * vec4(t.dot2, 1);
    dot3 = View * World * vec4(t.dot3, 1);
 
    glNormal3f(norm);
    glVertex3f(dot1.x, dot1.y, dot1.z);
    glVertex3f(dot2.x, dot2.y, dot3.z);
    glVertex3f(dot3.x, dot3.y, dot3.z);
}
glEnd();

由此产生的问题：为什么代码2和代码3得到的结果一样，而代码1和代码2却不同？

Code # 3
mat4 Proj = glFrustum(left, right, bottom, top, zNear, zFar);
mat4 View = gluLookAt(position, direction, up);
mat4 World = mat4(1);
glMatrixMode(GL_PROJECTION);
glLoadMatrix(Proj);
*glMatrixMode(GL_MODELVIEW);
glLoadMatrix(View);*
glBegin(GL_TRIANGLES);
for (auto& t : mesh)
{
    norm = World * vec4(t.norm, 0);
    dot1 = World * vec4(t.dot1, 1);
    dot2 = World * vec4(t.dot2, 1);
    dot3 = World * vec4(t.dot3, 1);
 
    glNormal3f(norm);
    glVertex3f(dot1.x, dot1.y, dot1.z);
    glVertex3f(dot2.x, dot2.y, dot3.z);
    glVertex3f(dot3.x, dot3.y, dot3.z);
}
glEnd();

告诉我我做错了什么？如何正确计算顶点乘以投影矩阵？

Answer 1

投影矩阵变换生成Homogeneous coordinates。齐次坐标有 4 个分量，但您只需将 3 个分量传递给顶点坐标。使用所有 4 个组件来指定顶点坐标。例如：

~~glVertex3f(dot1.x, dot1.y, dot1.z);~~

glVertex4f(dot1.x, dot1.y, dot1.z, dot1.w);

或

glVertex4fv(glm::value_ptr(dot1));

OpenGL。将顶点乘以投影矩阵

OpenGL. Multiplying a vertex by a projection matrix

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opengl