在现代opengl中旋转一个立方体......看起来很奇怪

Question

我有些失落，真的失落。

我正在尝试旋转一个立方体（现在只是围绕 y 轴），这是（丑陋和错误的）结果：

这是旋转矩阵的代码：

def rotate(axis: Vector3, angle: Float): Unit =
{
    val cosAngle: Float = Math.cos(angle).toFloat
    val sinAngle: Float = Math.sin(angle).toFloat

    val oneMinusCosAngle: Float = 1.0f - cosAngle

    val xy: Float = axis.x * axis.y
    val xz: Float = axis.x * axis.z

    val yz: Float = axis.y * axis.z

    val xs: Float = axis.x * sinAngle
    val ys: Float = axis.y * sinAngle
    val zs: Float = axis.z * sinAngle

    val f00: Float = axis.x * axis.x * oneMinusCosAngle + cosAngle
    val f01: Float = xy * oneMinusCosAngle + zs
    val f02: Float = xz * oneMinusCosAngle - ys

    val f10: Float = xy * oneMinusCosAngle - zs
    val f11: Float = axis.y * axis.y * oneMinusCosAngle + cosAngle
    val f12: Float = yz * oneMinusCosAngle + xs

    val f20: Float = xz * oneMinusCosAngle + ys
    val f21: Float = yz * oneMinusCosAngle - xs
    val f22: Float = axis.z * axis.z * oneMinusCosAngle + cosAngle

    val t00: Float = this.m00 * f00 + this.m10 * f01 + this.m20 * f02
    val t01: Float = this.m01 * f00 + this.m11 * f01 + this.m21 * f02
    val t02: Float = this.m02 * f00 + this.m12 * f01 + this.m22 * f02
    val t03: Float = this.m03 * f00 + this.m13 * f01 + this.m23 * f02
    val t10: Float = this.m00 * f10 + this.m10 * f11 + this.m20 * f12
    val t11: Float = this.m01 * f10 + this.m11 * f11 + this.m21 * f12
    val t12: Float = this.m02 * f10 + this.m12 * f11 + this.m22 * f12
    val t13: Float = this.m03 * f10 + this.m13 * f11 + this.m23 * f12

    this.m00 = t00
    this.m01 = t01
    this.m02 = t02
    this.m03 = t03

    this.m10 = t10
    this.m11 = t11
    this.m12 = t12
    this.m13 = t13

    this.m20 = this.m00 * f20 + this.m10 * f21 + this.m20 * f22
    this.m21 = this.m01 * f20 + this.m11 * f21 + this.m21 * f22
    this.m22 = this.m02 * f20 + this.m12 * f21 + this.m22 * f22
    this.m23 = this.m03 * f20 + this.m13 * f21 + this.m23 * f22
}

它的灵感来自：https://github.com/LWJGL/lwjgl/blob/master/src/java/org/lwjgl/util/vector/Matrix4f.java，它不再是 lwjgl 3 的一部分

立方体本身是由这些顶点、索引和纹理坐标组成的

val vertices: Array[Float] = Array(
    -0.5f,0.5f,-0.5f,
    -0.5f,-0.5f,-0.5f,
    0.5f,-0.5f,-0.5f,
    0.5f,0.5f,-0.5f,

    -0.5f,0.5f,0.5f,
    -0.5f,-0.5f,0.5f,
    0.5f,-0.5f,0.5f,
    0.5f,0.5f,0.5f,

    0.5f,0.5f,-0.5f,
    0.5f,-0.5f,-0.5f,
    0.5f,-0.5f,0.5f,
    0.5f,0.5f,0.5f,

    -0.5f,0.5f,-0.5f,
    -0.5f,-0.5f,-0.5f,
    -0.5f,-0.5f,0.5f,
    -0.5f,0.5f,0.5f,

    -0.5f,0.5f,0.5f,
    -0.5f,0.5f,-0.5f,
    0.5f,0.5f,-0.5f,
    0.5f,0.5f,0.5f,

    -0.5f,-0.5f,0.5f,
    -0.5f,-0.5f,-0.5f,
    0.5f,-0.5f,-0.5f,
    0.5f,-0.5f,0.5f
  )

  val indices: Array[Int] = Array(
    0,1,3,
    3,1,2,
    4,5,7,
    7,5,6,
    8,9,11,
    11,9,10,
    12,13,15,
    15,13,14,
    16,17,19,
    19,17,18,
    20,21,23,
    23,21,22
  )

  val textureCoords: Array[Float] = Array(
    0,0,
    0,1,
    1,1,
    1,0,

    0,0,
    0,1,
    1,1,
    1,0,

    0,0,
    0,1,
    1,1,
    1,0,

    0,0,
    0,1,
    1,1,
    1,0,

    0,0,
    0,1,
    1,1,
    1,0,

    0,0,
    0,1,
    1,1,
    1,0
  )

它的模型矩阵是这样计算的：

def calculateModelMatrix(position: Vector3, rotation: Vector3, scale: Float): Matrix4 =
{
    val matrix: Matrix4 = Matrix4.Identity
    matrix.translate(position)
    matrix.rotate(new Vector3(1,0,0), Math.toRadians(rotation.x).toFloat)
    matrix.rotate(new Vector3(0,1,0), Math.toRadians(rotation.y).toFloat)
    matrix.rotate(new Vector3(0,0,1), Math.toRadians(rotation.z).toFloat)
    matrix.scale(new Vector3(scale, scale, scale))

    matrix
}

从正面渲染立方体就像一个魅力。我还没有实现移动“相机”，所以也许 viewMatrix 是错误的？

ViewMatrix 计算每一帧（在相机中），如下所示：

def calculateViewMatrix(): Matrix4 =
{
    val matrix: Matrix4 = Matrix4.Identity
    matrix.rotate(new Vector3(1,0,0), Math.toRadians(this.pitch).toFloat)
    matrix.rotate(new Vector3(0,1,0), Math.toRadians(this.yaw).toFloat)
    matrix.translate(new Vector3(-this.position.x, -this.position.y, -this.position.z))
    matrix
}

如果您需要额外的代码，我可以提供一切，我只是不想发布所有代码并阻止很多人。

编辑：

根据 cmets 添加着色器代码和投影矩阵生成：

def calculateProjectionMatrix(): Matrix4 =
{
    val aspectRatio: Float = 1024 / 768 // TODO get this from somewhere
    val yScale: Float = ((1.0f / Math.tan(Math.toRadians(FOV / 2f))) * aspectRatio).toFloat
    val xScale: Float = yScale / aspectRatio
    val frustumLength = FAR_PLANE - NEAR_PLANE

    val matrix: Matrix4 = Matrix4.Zero
    matrix.m00 = xScale
    matrix.m11 = yScale
    matrix.m22 = -((FAR_PLANE + NEAR_PLANE) / frustumLength)
    matrix.m23 = -1.0f
    matrix.m32 = -((2.0f * NEAR_PLANE * FAR_PLANE) / frustumLength)

    matrix
}

（是的，窗口尺寸匹配 1024*768）

projectionMatrix 被设置一次，因为它永远不会改变。

着色器代码：

#version 330 core

in vec3 position;
in vec2 textureCoords;

out vec2 passTextureCoords;

uniform mat4 modelViewProjectionMatrix;

void main(void)
{
    gl_Position = modelViewProjectionMatrix * vec4(position, 1.0f);
    passTextureCoords = textureCoords;
}

并且，modelViewProjectionMatrix 会在每一帧中计算（并设置），如下所示：

modelViewProjectionMatrix = Matrix4.multiply(viewProjectionMatrix, modelMatrix)

viewProjetionMatrix 在哪里：

def calculateViewProjectionMatrix(): Matrix4 =
{
    Matrix4.multiply(this.projectionMatrix, this.viewMatrix)
}

而且，100% 确定，multiply-method...我们这里有一个对象（就像所有 java-devs 的静态方法）

def multiply(left: Matrix4, right: Matrix4): Matrix4 =
{
    val matrix: Matrix4 = new Matrix4(left)
    matrix.multiply(right)

    matrix
}

里面有一个copy-constructor，类实例的multiply-method是：

def multiply(right: Matrix4): Unit =
{
    set(
      this.m00 * right.m00 + this.m10 * right.m01 + this.m20 * right.m02 + this.m30 * right.m03,
      this.m01 * right.m00 + this.m11 * right.m01 + this.m21 * right.m02 + this.m31 * right.m03,
      this.m02 * right.m00 + this.m12 * right.m01 + this.m22 * right.m02 + this.m32 * right.m03,
      this.m03 * right.m00 + this.m13 * right.m01 + this.m23 * right.m02 + this.m33 * right.m03,
      this.m00 * right.m10 + this.m10 * right.m11 + this.m20 * right.m12 + this.m30 * right.m13,
      this.m01 * right.m10 + this.m11 * right.m11 + this.m21 * right.m12 + this.m31 * right.m13,
      this.m02 * right.m10 + this.m12 * right.m11 + this.m22 * right.m12 + this.m32 * right.m13,
      this.m03 * right.m10 + this.m13 * right.m11 + this.m23 * right.m12 + this.m33 * right.m13,
      this.m00 * right.m20 + this.m10 * right.m21 + this.m20 * right.m22 + this.m30 * right.m23,
      this.m01 * right.m20 + this.m11 * right.m21 + this.m21 * right.m22 + this.m31 * right.m23,
      this.m02 * right.m20 + this.m12 * right.m21 + this.m22 * right.m22 + this.m32 * right.m23,
      this.m03 * right.m20 + this.m13 * right.m21 + this.m23 * right.m22 + this.m33 * right.m23,
      this.m00 * right.m30 + this.m10 * right.m31 + this.m20 * right.m32 + this.m30 * right.m33,
      this.m01 * right.m30 + this.m11 * right.m31 + this.m21 * right.m32 + this.m31 * right.m33,
      this.m02 * right.m30 + this.m12 * right.m31 + this.m22 * right.m32 + this.m32 * right.m33,
      this.m03 * right.m30 + this.m13 * right.m31 + this.m23 * right.m32 + this.m33 * right.m33
    )
  }

其中 set(...) 只是设置 Matrix4 的 var(iable)... 所以第一行是 m00，最后一行是 m33。

def set(  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): Unit =
  {
    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
  }

也许乘法是错误的（可能是，但对我来说真的很奇怪，因为我之前验证过）

Answer 1

将您的Matrix.rotate 代码与链接代码进行比较，您首先要这样做

this.m00 = t00

然后你再做

this.m20 = this.m00 * f20 + this.m10 * f21 + this.m20 * f22

使用您刚刚修改的 this.m00。您以类似的方式执行此操作几次。示例代码以相反的方式执行此操作，这意味着最终结果不同。交换代码块，一切都应该没问题。我希望 LWJGL 很快会决定重新添加线性代数类！