Question

我创建了一个可以删除边的自定义多维数据集。我最终想把立方体打印到纸质打印机上。我想通过使用OpenGL旋转方法的输出来进行自己的旋转。

我的问题：在轮换后是否存在描述Identity Matrix的文档？或者是可用于OpenGL旋转方法的源？

Answer 1

glRotate创建一个旋转矩阵，并将其放在当前矩阵堆栈顶部的矩阵上。旋转矩阵在线性代数中是众所周知的。

Answer 2

您可以在互联网上阅读有关矩阵计算和矩阵变换的信息，这里有几个链接。

虽然这是我为计算你想要计算的东西而创建的东西。没有太多解释，因为它基本上只是一堆数学公式。

public class Matrix4
{
    public float m00, m01, m02, m03;
    public float m10, m11, m12, m13;
    public float m20, m21, m22, m23;
    public float m30, m31, m32, m33;

    public Matrix4()
    {
        this.set(
            1f, 0f, 0f, 0f,
            0f, 1f, 0f, 0f,
            0f, 0f, 1f, 0f,
            0f, 0f, 0f, 1f);
    }

    public void rotate(float angle, float x, float y, float z)
    {
        float sin = (float) Math.sin(angle);
        float cos = (float) Math.cos(angle);

        if ((x * x + y * y + z * z) != 1f)
        {
            float length = (float) Math.sqrt(x * x + y * y + z * z);

            if (length > 0f)
            {
                length = 1f / length;

                x *= length;
                y *= length;
                z *= length;
            }
        }

        this.mul(
            x * x * (1f - cos) + cos, x * y * (1f - cos) - z * sin, x * z * (1f - cos) + y * sin, 0f,
            y * x * (1f - cos) + z * sin, y * y * (1f - cos) + cos, y * z * (1f - cos) - x * sin, 0f,
            x * z * (1f - cos) - y * sin, y * z * (1f - cos) + x * sin, z * z * (1f - cos) + cos, 0f,
            0f, 0f, 0f, 1f);
    }

    public void mul(
            float m00, float m01, float m02, float m03,
            float m10, float m11, float m12, float m13,
            float m20, float m21, float m22, float m23,
            float m30, float m31, float m32, float m33)
    {
        float mm00 = this.m00 * m00 + this.m01 * m10 + this.m02 * m20 + this.m03 * m30;
        float mm01 = this.m00 * m01 + this.m01 * m11 + this.m02 * m21 + this.m03 * m31;
        float mm02 = this.m00 * m02 + this.m01 * m12 + this.m02 * m22 + this.m03 * m32;
        float mm03 = this.m00 * m03 + this.m01 * m13 + this.m02 * m23 + this.m03 * m33;

        float mm10 = this.m10 * m00 + this.m11 * m10 + this.m12 * m20 + this.m13 * m30;
        float mm11 = this.m10 * m01 + this.m11 * m11 + this.m12 * m21 + this.m13 * m31;
        float mm12 = this.m10 * m02 + this.m11 * m12 + this.m12 * m22 + this.m13 * m32;
        float mm13 = this.m10 * m03 + this.m11 * m13 + this.m12 * m23 + this.m13 * m33;

        float mm20 = this.m20 * m00 + this.m21 * m10 + this.m22 * m20 + this.m23 * m30;
        float mm21 = this.m20 * m01 + this.m21 * m11 + this.m22 * m21 + this.m23 * m31;
        float mm22 = this.m20 * m02 + this.m21 * m12 + this.m22 * m22 + this.m23 * m32;
        float mm23 = this.m20 * m03 + this.m21 * m13 + this.m22 * m23 + this.m23 * m33;

        float mm30 = this.m30 * m00 + this.m31 * m10 + this.m32 * m20 + this.m33 * m30;
        float mm31 = this.m30 * m01 + this.m31 * m11 + this.m32 * m21 + this.m33 * m31;
        float mm32 = this.m30 * m02 + this.m31 * m12 + this.m32 * m22 + this.m33 * m32;
        float mm33 = this.m30 * m03 + this.m31 * m13 + this.m32 * m23 + this.m33 * m33;

        this.m00 = mm00; this.m01 = mm01; this.m02 = mm02; this.m03 = mm03;
        this.m10 = mm10; this.m11 = mm11; this.m12 = mm12; this.m13 = mm13;
        this.m20 = mm20; this.m21 = mm21; this.m22 = mm22; this.m23 = mm23;
        this.m30 = mm30; this.m31 = mm31; this.m32 = mm32; this.m33 = mm33;
    }

    public void set(
            float m00, float m01, float m02, float m03,
            float m10, float m11, float m12, float m13,
            float m20, float m21, float m22, float m23,
            float m30, float m31, float m32, float m33)
    {
        this.m00 = m00;
        this.m01 = m01;
        this.m02 = m02;
        this.m03 = m03;

        this.m10 = m10;
        this.m11 = m11;
        this.m12 = m12;
        this.m13 = m13;

        this.m20 = m20;
        this.m21 = m21;
        this.m22 = m22;
        this.m23 = m23;

        this.m30 = m30;
        this.m31 = m31;
        this.m32 = m32;
        this.m33 = m33;
    }
}

以下内容将创建一个身份矩阵Matrix4 m = new Matrix4();

重要注意rotate() Matrix4函数中给出的角度是弧度，在OpenGL中glRotate()函数要求角度为度。

此外，如果Matrix是“相反”，当您使用它时，在您使用Matrix之前，只需计算Transpose of the matrix，然后就可以使用它。

需要描述OpenGL旋转方法输出的文档

2 个答案: