OpenGL. Multiplying a vertex by a projection matrix

I’m trying to draw a model and this is what I ran into, the code below works like 2d, although there should be a perspective

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();

And so the perspective appears:

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();

From which the question arose: why code 2 and code 3 get the same result, but code 1 and code 2 are different?

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();

Tell me what am I doing wrong? How can I calculate the vertex multiplied by the projection matrix correctly?

>Solution :

The transformation with the projection matrix generates Homogeneous coordinates. A Homogeneous coordinate has 4 components, but you just pass 3 components to the vertex coordinate. Use all 4 components to specify the vertex coordinate. e.g:

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

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

or

glVertex4fv(glm::value_ptr(dot1));