矩陣轉換問題 - Z軸旋轉是歪斜的

Question

對於簡單的2D遊戲，我正在嘗試使用矩陣圍繞Z軸旋轉精靈。我顯然做錯了，因爲當我試圖旋轉我的精靈時，它看起來像圍繞着屏幕原點（底部，左邊）旋轉而不是精靈原點。我很困惑，因爲我的四連桿已經在原點了，所以我不認爲我需要翻譯 - >旋轉並翻譯回來。這裏有一個代碼段和一個小視頻或erroneous transformation

void MatrixMultiply(
MATRIX  &mOut, 
const MATRIX &mA, 
const MATRIX &mB); 
/*!*************************************************************************** 
@Function   TransTransformArray 
@Output   pTransformedVertex Destination for transformed vectors 
@Input    pV     Input vector array 
@Input    nNumberOfVertices Number of vectors to transform 
@Input    pMatrix    Matrix to transform the vectors of input vector (e.g. use 1 for position, 0 for normal) 
@Description  Transform all vertices in pVertex by pMatrix and store them in 
       pTransformedVertex 
       - pTransformedVertex is the pointer that will receive transformed vertices. 
       - pVertex is the pointer to untransformed object vertices. 
       - nNumberOfVertices is the number of vertices of the object. 
       - pMatrix is the matrix used to transform the object. 
*****************************************************************************/ 
void TransTransformArray(
VECTOR3  * const pTransformedVertex, 
const VECTOR3 * const pV, 
const int  nNumberOfVertices, 
const MATRIX * const pMatrix); 


RenderQuad CreateRenderQuad(
    const Texture2D & texture, 
    float x, 
    float y, 
    float scaleX, 
    float scaleY, 
    float rotateRadians, 
    int zIndex, 
    const Color & color, 
    const Quad2 & textureCoord, 
    const char * name 
) { 
    MATRIX mT; 
    MATRIX mS; 
    MATRIX concat; 
    MATRIX mR; 

    MatrixTranslation(mT, x, y, 0.0f); 
    MatrixRotationZ(mR, rotateRadians); 
    MatrixScaling(mS, scaleX, scaleY, 1.0f); 

    VECTOR3 quad[] = { 
     {-0.5f, 0.5f, 0.f}, //tl 
     {0.5f, 0.5f, 0.f}, //tr 
     {-0.5, -0.5f, 0.0f}, //bl 
     {0.5f, -0.5f, 0.0f}, //br 
    }; 

    MatrixMultiply(concat, mR, mT); 
    MatrixMultiply(concat, concat, mS); 
    // apply to all the points in the quad 
    TransTransformArray(quad, quad, 4, &concat); 

==更新：

這裏的結構和渲染代碼：

我使用的是矩陣類從oolongengine code.google我轉換所有的四邊形，然後使用OpenGL渲染它們。這裏是我的數據結構和渲染代碼：

typedef struct _RenderData { 
    VECTOR3  vertex; 
    RenderColor3D  color; 
    RenderTextureCoord textureCoord; 
    float    zIndex; 
    GLuint    textureId; 
} RenderData; 

typedef struct _RenderQuad { 
    //! top left 
    RenderData tl; 
    //! top right 
    RenderData tr; 
    //! bottom left 
    RenderData bl;   
    //! bottom right 
    RenderData br; 

    float zIndex; 

    Texture2D * texture; // render quad draws a source rect from here 

    ESpriteBlendMode blendMode; 

} RenderQuad ; 

/// Draw 
class QuadBatch { 
    GLushort *    m_indices; 
    const Texture2D *  m_texture; 
    GLuint     m_vbos[2]; 
    RenderData *   m_vertices; 
}; 

QuadBatch::Draw() { 
    int offset = (int)&m_vertices[startIndex]; 

      // vertex 
      int diff = offsetof(RenderData, vertex); 
      glVertexPointer(3, GL_FLOAT, kRenderDataSize, (void*) (offset + diff)); 

      // color 
      diff = offsetof(RenderData, color); 
      glColorPointer(4, GL_FLOAT, kRenderDataSize, (void*)(offset + diff)); 

      // tex coords 
      diff = offsetof(RenderData, textureCoord); 
      glTexCoordPointer(2, GL_FLOAT, kRenderDataSize, (void*)(offset + diff)); 

      // each quad has 6 indices 

      glDrawElements(GL_TRIANGLES, vertexCount * elementMultiplier, GL_UNSIGNED_SHORT, m_indices); 

Answer 1

'旋轉'，根據定義，圍繞原點（0,0,0）。如果你想要一個不同的旋轉軸，你必須應用一個翻譯組件。假設你想圍繞軸a應用旋轉R。以適用於任意的矢量x的變換是：

X - >一個+ R（X - A）= RX +（A - Ra）爲

（這可能需要一些盯着消化）。所以，在之後應用你的旋轉 - 如你所觀察到的那樣，圍繞原點旋轉 - 你必須添加常量向量（a-Ra）。

[編輯：]這個答案是語言和平臺不可知的 - 無論你在哪裏看，數學都是一樣的。特定的庫包含不同的結構和API來應用轉換。例如，DirectX和OpenGL都保持4x4矩陣變換，以將旋轉和平移統一爲單個矩陣乘法（通過稱爲齊次座標的設備）。