Switching from orthogonal to perspective projection - c++

Question

I am trying to add a paralax effect to an existing engine. So far the engine worked with an orthogonal projection. Objects are placed in pixel coordinates on the screen. The problem is that I can not figure out how to replicate the same projection with a perspective projection matrix ect. that I can add a Z coordinate for depth.
I tried various combinations of matrices and z coordinates already and the result was always a black screen.
The matrix I am trying to replace:
glm::mat4 projection = glm::ortho(0.0f, static_cast<GLfloat>(1280.0f), static_cast<GLfloat>(720.0f), 0.0f, 0.0f, -100.0f);
The vertex shader:
// Shader code (I tested this while having identity matrices for view and model
#version 330 core
layout (location = 0) in vec2 vertex;
uniform mat4 projection;
uniform mat4 view;
uniform mat4 model;
void main() {
gl_Position = projection * view * model * vec4(vertex.xy, 1.0f, 1.0f);
}
The projection code I thought might work:
glm::mat4 model = glm::mat4(1.0f);
model = glm::translate(model, glm::vec3(-640, -310.0f, 0.0f));
model = glm::scale(model, glm::vec3(1.0f / 1280.0f, 1.0f / 720.0f, 1.0f));
glm::vec3 cameraPos = glm::vec3(0.0f, 0.0f, 0.0f);
glm::vec3 cameraFront = glm::vec3(0.0f, 0.0f, -1.0f);
glm::vec3 cameraUp = glm::vec3(0.0f, 1.0f, 0.0f);
glm::mat4 view = glm::lookAt(cameraPos, cameraPos + cameraFront, cameraUp);
glm::mat4 projection = glm::perspective(glm::radians(45.0f), 1.0f, 0.1f, -100.0f);
Expected Is that a rectangle gets still displayed at similar position (I can correct the details once something works) without having a black screen.

Answer 1

The specification of the Perspective projection matrix is wrong.
glm::perspective(glm::radians(45.0f), 1.0f, 0.1f, -100.0f);
glm::perspective defines a Viewing frustum by an field of view angle along the y axis, an aspect ratio and a distance to the near and the far plane.
So the near and the far plane have to be positive values (> 0) and near has to be less than far:
0 < near < far
e.g.:
glm::perspective(glm::radians(45.0f), 1.0f, 0.1f, 100.0f);
The geometry has to be in between the near and the far plane, else it is clipped.
The ration of the size of the projected area and the depth is linear and can be calculated. It depends on the field of view angle:
float fov_y = glm::radians(45.0f);
float ratio_size_depth = tan(fov_y / 2.0f) * 2.0f;
Note, if an object should appear with half the size in the projection on the viewport, the distance from the object to the camera (depth) has to be doubled.

Answer 2

So the corrected model translation matrix and required depth in the shader to have the coordinates match on the plane are as follows:
int width = 1280.0f;
int height = 720.0f;
glm::mat4 model = glm::mat4(1.0f);
model = glm::scale(model, glm::vec3(-1.0f / width, -1.0f / height, 1.0f));
model = glm::translate(model, glm::vec3(-((float)width / 2.0f), -((float)height / 2.0f), 0.0f));
glm::vec3 cameraPos = glm::vec3(0.0f, 0.0f, 0.0f);
glm::vec3 cameraFront = glm::vec3(0.0f, 0.0f, 1.0f);
glm::vec3 cameraUp = glm::vec3(0.0f, 1.0f, 0.0f);
glm::mat4 view = glm::lookAt(cameraPos, cameraPos + cameraFront, cameraUp);
glm::mat4 projection = glm::perspective(glm::radians(45.0f), 1.0f, 0.1f, 100.0f);
Shader with Z-Value:
#version 330 core
layout (location = 0) in vec2 vertex;
uniform mat4 projection;
uniform mat4 view;
uniform mat4 model;
void main() {
gl_Position = projection * view * model * vec4(vertex.xy, 1.208f, 1.0f);
}
Which will be equivalent tho this orthogonal matrix:
glm::mat4 model = glm::mat4(1.0f);
glm::mat4 view = glm::mat4(1.0f);
glm::mat4 projection = glm::ortho(0.0f, static_cast<GLfloat>(this->width), static_cast<GLfloat>(this->height), 0.0f, 0.0f, -100.0f);
The matrices can also be multiplied together to have only one projection matrix you pass to the shader. This will make it easier to have an actual model matrix passed with the mesh ect.