三维坐标系与几何学.htm

此文件是微软MSDN中d3d部分资料的翻译文件

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style="FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-fareast-language: ZH-CN">将两个四元数的合成应用于几何体意味着“把几何体绕<SPAN 
lang=EN-US>axis<SUB>2</SUB>轴旋转rotation<SUB>2</SUB>角度，然后绕axis<SUB>1</SUB>轴旋转rotation<SUB>1</SUB>角度”。在这种情况下，Q表示绕单根轴的旋转，该旋转是先后将q<SUB>2</SUB>和q<SUB>1</SUB>应用于几何体的结果。<o:p></o:p></SPAN></SPAN></P>
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style="FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-fareast-language: ZH-CN">使用四元数，应用程序可以计算出一条从一根轴和一个方向到另一根轴和另一个方向的平滑、合理的路径。因此，在<SPAN 
lang=EN-US>q<SUB>1</SUB>和q<SUB>2</SUB>间插值提供了一个从一个方向变化到另一个方向的简单方法。<o:p></o:p></SPAN></SPAN></P>
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style="FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-fareast-language: ZH-CN">当同时使用合成与插值时，四元数提供了一个看似复杂而实际简单的操作几何体的方法。例如，设想我们希望把一个几何体旋转到某个给定方向。我们已经知道希望将它绕<SPAN 
lang=EN-US>axis<SUB>2</SUB>轴旋转r<SUB>2</SUB>度，然后绕axis<SUB>1</SUB>轴旋转r<SUB>1</SUB>度，但是我们不知道最终的四元数。通过使用合成，我们可以在几何体上合成两个旋转并得到最终单个的四元数。然后，我们可以在原始四元数和合成的四元数间进行插值，得到两者之间的平滑转换。<o:p></o:p></SPAN></SPAN></P>
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style="FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-fareast-language: ZH-CN">Direct3D扩展（D3DX）工具库包含了帮助用户使用四元数的函数。例如，<U>D3DXQuaternionRotationAxis</U>函数给一个定义旋转轴的向量增加一个旋转值，并在由<U>D3DXQUTERNION</U>结构定义的四元数中返回结果。另外，<U>D3DXQuaternionMultiply</U>函数合成四元数，<U>D3DXQuaternionSlerp</U>函数在两个四元数间进行球面线性插值（spherical 
linear interpolation）。<o:p></o:p></SPAN></P>
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style="FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-fareast-language: ZH-CN">Direct3D应用程序可以使用下列函数简化对四元数的使用。<o:p></o:p></SPAN></P>
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style="FONT-FAMILY: 宋体; mso-bidi-font-family: 宋体; mso-fareast-language: ZH-CN">Direct3D应用程序可以使用下列函数简化对三成员向量的使用。<o:p></o:p></SPAN></P>
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