这是一个正确的透视矩阵吗？

Question

我有一个透视fov，但在旋转时，它不会“看起来”校正 - 更远的物体比更接近的物体更快，将它们传递在屏幕的中间。

所以：这是正确的吗？如果重要的话，使用右手坐标？

    public static Matrix4x4 PerspectiveFOV(float fov, float aspect, float near, float far)
    {
        float yScale = 1.0F / (float)Math.Tan(fov / 2);
        float xScale = yScale / aspect;
        float farmnear = far - near;
        return new Matrix4x4(
            xScale, 0, 0, 0,
            0, yScale, 0, 0,
            0, 0, far / (farmnear), 1,
            0, 0, -near * (far / (farmnear)), 1
            );
    }

.

谢谢。

Answer 1

I see a couple of problems. First, the argument to tan() should be converted from degrees to radians.

Second, the formula for perspective projection in OpenGL is a little different from yours. As specified here, it uses 'near - far' in the denominator instead of your 'far - near'. The numerator terms are also different. Modifying your function slightly and converting from Java to C, I produced a projection matrix identical to the one given by gluPerspective() with the following:

static void my_PerspectiveFOV(double fov, double aspect, double near, double far, double* mret) {
    double D2R = M_PI / 180.0;
    double yScale = 1.0 / tan(D2R * fov / 2);
    double xScale = yScale / aspect;
    double nearmfar = near - far;
    double m[] = {
        xScale, 0, 0, 0,
        0, yScale, 0, 0,
        0, 0, (far + near) / nearmfar, -1,
        0, 0, 2*far*near / nearmfar, 0 
    };
    geom_matrix4_copy(m, mret);
}

Answer 2

For questions such as this one I would suggest an excellent resources: https://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix It really goes in the detail of the projection matrix. They are more lessons on the topic of camera, constructing camera rays, etc. You will need to do some digging.