Matrix4x4.Perspective

Parameters

Returns

Matrix4x4 The projection matrix.

Description

Create a perspective projection matrix.

Projection matrices in Unity follow OpenGL convention, i.e. clip space near plane is at z=-1, and far plane is at z=1.

The returned matrix embeds a z-flip operation whose purpose is to cancel the z-flip performed by the camera view matrix. If the view matrix is an identity or some custom matrix that doesn't perform a z-flip, consider multiplying the third column of the projection matrix (i.e. m02, m12, m22 and m32) by -1.

Note that depending on the graphics API used, projection matrices in shaders can follow different convention, for example the D3D-style clip space has near plane at zero and far plane at one; and "reversed Z" projection has near plane at one and far plane at zero. To calculate projection matrix value suitable for passing to shader variables, use GL.GetGPUProjectionMatrix.

using UnityEngine;

public class ExampleScript : MonoBehaviour
{
    void Start()
    {
        // create projection matrix: 60 FOV, square aspect,
        // near plane 1, far plane 100
        var matrix = Matrix4x4.Perspective(60, 1, 1, 100);
        // will print:
        // 0.20000 0.00000  0.00000  0.00000
        // 0.00000 0.20000  0.00000  0.00000
        // 0.00000 0.00000 -0.02020 -1.02020
        // 0.00000 0.00000  0.00000  1.00000
        Debug.Log("projection matrix\n" + matrix);

        // get shader-compatible projection matrix value
        var shaderMatrix = GL.GetGPUProjectionMatrix(matrix, false);
        // on a Direct3D-like graphics API, will print:
        // 0.20000 0.00000 0.00000 0.00000
        // 0.00000 0.20000 0.00000 0.00000
        // 0.00000 0.00000 0.01010 1.01010
        // 0.00000 0.00000 0.00000 1.00000
        Debug.Log("shader projection matrix\n" + shaderMatrix);
    }
}

Additional resources: Ortho, Camera.projectionMatrix, GL.LoadPixelMatrix, GL.LoadProjectionMatrix, GL.GetGPUProjectionMatrix.