这是正确的视角 FOV 矩阵吗？

发布于 2024-11-08 14:35:47 字数 560 浏览 0 评论 0原文

我有一个透视视野，但旋转时，它“看起来”不正确 - 较远的物体比较近的物体移动得更快，将它们从屏幕中间经过。

那么：这是正确的吗？使用右手坐标，如果这很重要的话？

    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。

原文

I have a perspective FOV, but when rotating, it doesn't "look" correct - Farther objects traverse faster than closer objects, passing them in the middle of the screen.

So: Is this correct? Using right-handed coordinates, if that matters?

    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
            );
    }

Thanks.

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陌生 2024-11-15 14:35:47

我看到了几个问题。
首先， tan() 的参数应从度数转换为弧度。

其次，OpenGL中透视投影的公式与你的有点不同。正如此处所指定的，它在分母中使用“近-远”而不是您的“远-近'。分子项也不同。稍微修改一下你的函数并从 Java 转换为 C，我生成了一个与 gluPerspective() 给出的投影矩阵相同的投影矩阵，其中包含以下内容：

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);
}

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);
}

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