OpenGL 奇怪的立方体旋转

Question

我正在自学现代 OpenGL。我目前运行在渲染 3D 立方体时遇到问题。

首先我创建了一个精灵，这是我的 class 包含位置、宽度、高度和单个矩形精灵的纹理。然后我将它传递给我的渲染器 class 来创建一个立方体，它的每面墙都由相同的精灵组成。

        void Renderer::constructWall(maths::vec3 bottomLeft, maths::vec3 topLeft, maths::vec3 topRight, maths::vec3 bottomRight, maths::vec4 color){
        m_Buffer->position = bottomLeft;
        m_Buffer->color = maths::vec4(color.x, color.y, color.z, 1.0f);
        m_Buffer->tex = maths::vec2(0.0f, 0.0f);
        m_Buffer++;

        m_Buffer->position = topLeft;
        m_Buffer->color = maths::vec4(color.x, color.y, color.z, 1.0f);
        m_Buffer->tex = maths::vec2(0.0f, 1.0f);
        m_Buffer++;

        m_Buffer->position = topRight;
        m_Buffer->color = maths::vec4(color.x, color.y, color.z, 1.0f);
        m_Buffer->tex = maths::vec2(1.0f, 1.0f);
        m_Buffer++;

        m_Buffer->position = bottomRight;
        m_Buffer->color = maths::vec4(color.x, color.y, color.z, 1.0f);
        m_Buffer->tex = maths::vec2(1.0f, 0.0f);
        m_Buffer++;

        m_IndexCount += 6;
    }

m_Buffer是一个VertexData类型的指针，是一个struct:

        struct VertexData{
        maths::vec3 position;
        maths::vec4 color;
        maths::vec2 tex;
    };

m_IndexCount 是一个简单的计数器，用于计算当我在渲染器 class 中提交刷新时需要渲染的索引数。我通过对立方体的顶点建模并以这种方式使用 constructWall 函数来创建立方体：

        maths::vec3 A(vertex.x, vertex.y, -depth/2);
        maths::vec3 B(vertex.x, vertex.y + size.y, -depth / 2);
        maths::vec3 C(vertex.x + size.x, vertex.y + size.y, -depth / 2);
        maths::vec3 D(vertex.x + size.x, vertex.y, -depth / 2);
        maths::vec3 E(vertex.x, vertex.y, depth/2);
        maths::vec3 F(vertex.x, vertex.y + size.y, depth/2);
        maths::vec3 G(vertex.x + size.x, vertex.y + size.y, depth/2);
        maths::vec3 H(vertex.x + size.x, vertex.y, depth/2);
        constructWall(A, B, C, D, color1);
        constructWall(E, F, G, H, color1);
        constructWall(A, B,F,E, color1);
        constructWall(D, C, G, H, color1);
        constructWall(A, E, H, D, color1);
        constructWall(B, F, G, C, color1);

当我创建一个立方体时它工作得很好，在一个轴上旋转它也可以，但是当我尝试在多个轴上旋转它时，我的立方体有时会表现得很奇怪：

来源：http://imgur.com/fI3s9fC

还有我的矩阵码：

        mat4::mat4()
    {
        for (int i = 0; i < 4 * 4; i++)
            elements[i] = 0.0f;
    }

    mat4::mat4(float diagonal)
    {
        for (int i = 0; i < 4 * 4; i++)
            elements[i] = 0.0f;

        elements[0 + 0 * 4] = diagonal;
        elements[1 + 1 * 4] = diagonal;
        elements[2 + 2 * 4] = diagonal;
        elements[3 + 3 * 4] = diagonal;
    }

    mat4 mat4::identity()
    {
        return mat4(1.0f);
    }

    mat4& mat4::multiply(const mat4& other)
    {
        float data[16];
        for (int y = 0; y < 4; y++)
        {
            for (int x = 0; x < 4; x++)
            {
                float sum = 0.0f;
                for (int e = 0; e < 4; e++)
                {
                    sum += elements[x + e * 4] * other.elements[e + y * 4];
                }
                data[x + y * 4] = sum;
            }
        }
        memcpy(elements, data, 4 * 4 * sizeof(float));

        return *this;
    }

    vec3 mat4::multiply(const vec3& other) const
    {
        return vec3(
            columns[0].x * other.x + columns[1].x * other.y + columns[2].x * other.z + columns[3].x,
            columns[0].y * other.x + columns[1].y * other.y + columns[2].y * other.z + columns[3].y,
            columns[0].z * other.x + columns[1].z * other.y + columns[2].z * other.z + columns[3].z
            );
    }

    vec4 mat4::multiply(const vec4& other) const
    {
        return vec4(
            columns[0].x * other.x + columns[1].x * other.y + columns[2].x * other.z + columns[3].x * other.w,
            columns[0].y * other.x + columns[1].y * other.y + columns[2].y * other.z + columns[3].y * other.w,
            columns[0].z * other.x + columns[1].z * other.y + columns[2].z * other.z + columns[3].z * other.w,
            columns[0].w * other.x + columns[1].w * other.y + columns[2].w * other.z + columns[3].w * other.w
            );
    }

    mat4 operator*(mat4 left, const mat4& right)
    {
        return left.multiply(right);
    }

    mat4& mat4::operator*=(const mat4& other)
    {
        return multiply(other);
    }

    vec3 operator*(const mat4& left, const vec3& right)
    {
        return left.multiply(right);
    }

    vec4 operator*(const mat4& left, const vec4& right)
    {
        return left.multiply(right);
    }

    mat4 mat4::orthographic(float left, float right, float bottom, float top, float near, float far)
    {
        mat4 result(1.0f);

        result.elements[0 + 0 * 4] = 2.0f / (right - left);

        result.elements[1 + 1 * 4] = 2.0f / (top - bottom);

        result.elements[2 + 2 * 4] = 2.0f / (near - far);

        result.elements[0 + 3 * 4] = (left + right) / (left - right);
        result.elements[1 + 3 * 4] = (bottom + top) / (bottom - top);
        result.elements[2 + 3 * 4] = (far + near) / (far - near);

        return result;
    }

    mat4 mat4::perspective(float fov, float aspectRatio, float near, float far)
    {
        mat4 result(1.0f);

        float q = 1.0f / tan(toRadians(0.5f * fov));
        float a = q / aspectRatio;

        float b = (near + far) / (near - far);
        float c = (2.0f * near * far) / (near - far);

        result.elements[0 + 0 * 4] = a;
        result.elements[1 + 1 * 4] = q;
        result.elements[2 + 2 * 4] = b;
        result.elements[3 + 2 * 4] = -1.0f;
        result.elements[2 + 3 * 4] = c;

        return result;
    }

    mat4 mat4::translation(const vec3& translation)
    {
        mat4 result(1.0f);

        result.elements[0 + 3 * 4] = translation.x;
        result.elements[1 + 3 * 4] = translation.y;
        result.elements[2 + 3 * 4] = translation.z;

        return result;
    }

    mat4 mat4::rotation(float angle, const vec3& axis)
    {
        mat4 result(1.0f);

        float r = toRadians(angle);
        float c = cos(r);
        float s = sin(r);
        float omc = 1.0f - c;

        float x = axis.x;
        float y = axis.y;
        float z = axis.z;

        result.elements[0 + 0 * 4] = x * omc + c;
        result.elements[1 + 0 * 4] = y * x * omc + z * s;
        result.elements[2 + 0 * 4] = x * z * omc - y * s;

        result.elements[0 + 1 * 4] = x * y * omc - z * s;
        result.elements[1 + 1 * 4] = y * omc + c;
        result.elements[2 + 1 * 4] = y * z * omc + x * s;

        result.elements[0 + 2 * 4] = x * z * omc + y * s;
        result.elements[1 + 2 * 4] = y * z * omc - x * s;
        result.elements[2 + 2 * 4] = z * omc + c;

        return result;
    }

    mat4 mat4::scale(const vec3& scale)
    {
        mat4 result(1.0f);

        result.elements[0 + 0 * 4] = scale.x;
        result.elements[1 + 1 * 4] = scale.y;
        result.elements[2 + 2 * 4] = scale.z;

        return result;
    }

Answer 1

在您的代码中计算围绕任意轴旋转的对角线元素的公式似乎有误。尝试更改为：

    result.elements[0 + 0 * 4] = x * x + (1.0f - (x * x)) * c;
    result.elements[1 + 0 * 4] = y * x * omc + z * s;
    result.elements[2 + 0 * 4] = x * z * omc - y * s;

    result.elements[0 + 1 * 4] = x * y * omc - z * s;
    result.elements[1 + 1 * 4] = y * y + (1.0f - (y * y)) * c;
    result.elements[2 + 1 * 4] = y * z * omc + x * s;

    result.elements[0 + 2 * 4] = x * z * omc + y * s;
    result.elements[1 + 2 * 4] = y * z * omc - x * s;
    result.elements[2 + 2 * 4] = z * z + (1.0f - (z * z)) * c;

参考本文第 5.2 节mathematical explanation。

OpenGL 奇怪的立方体旋转

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