Version: 2020.2
  • C#


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public static Matrix4x4 Perspective(float fov, float aspect, float zNear, float zFar);


fov Vertical field-of-view in degrees.
aspect Aspect ratio (width divided by height).
zNear Near depth clipping plane value.
zFar Far depth clipping plane value.


Matrix4x4 The projection matrix.


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); } }