3.2 坐标系统及其变换.htm

计算机图形学教程计算机图形学教程

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style="mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman">θ</SPAN></FONT></P>
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face=楷体_GB2312 size=4>y</FONT></SPAN><FONT face=楷体_GB2312 size=4><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">＝</SPAN><SPAN 
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style="mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman">θ</SPAN></FONT></P>
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<P class=MsoNormal><SPAN 
style="mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman"><FONT 
face=楷体_GB2312 size=4>球坐标系统与直角坐标系统的关系为</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN-LEFT: 42pt"><SPAN lang=EN-US><FONT 
face=楷体_GB2312 size=4>x</FONT></SPAN><FONT face=楷体_GB2312 size=4><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">＝</SPAN><SPAN 
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style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">φ</SPAN><SPAN 
lang=EN-US>cos</SPAN><SPAN 
style="mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman">θ</SPAN></FONT></P>
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face=楷体_GB2312 size=4>y</FONT></SPAN><FONT face=楷体_GB2312 size=4><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">＝</SPAN><SPAN 
lang=EN-US>rsin</SPAN><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">φ</SPAN><SPAN 
lang=EN-US>sin</SPAN><SPAN 
style="mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman">θ</SPAN></FONT></P>
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face=楷体_GB2312 size=4>z</FONT></SPAN><FONT face=楷体_GB2312 size=4><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">＝</SPAN><SPAN 
lang=EN-US>rcos</SPAN><SPAN 
style="mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman">φ</SPAN></FONT></P>
<P class=MsoNormal><SPAN 
style="mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman"><FONT 
face=楷体_GB2312 size=4>这些坐标系统的定义与大家在空间解析几何中所熟知的定义是一致的。</FONT></SPAN></P>
<P class=MsoNormal><SPAN style="mso-spacerun: yes"><FONT face=楷体_GB2312 
size=4>&nbsp;&nbsp;&nbsp; </FONT></SPAN><FONT face=楷体_GB2312 size=4><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">另外，在计算机图形学中，为了通过显示设备来考察几何物体的特性，引入了一系列用于显示输出的坐标系统，这些坐标系统包括：</SPAN></FONT></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN style="mso-spacerun: yes"><FONT 
face=楷体_GB2312 size=4>&nbsp;&nbsp;&nbsp; </FONT></SPAN><FONT face=楷体_GB2312 
size=4>1)</FONT></SPAN><FONT face=楷体_GB2312 size=4><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">世界坐标系</SPAN><SPAN 
lang=EN-US>(world coordinate Systems)</SPAN><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，该坐标系统主要用于计算机图形场景中的所有图形对象的空间定位和定义，包括观察者的位置、视线等等。计算机图形系统中涉及的其它坐标系统都是参照它进行定义。</SPAN></FONT></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN style="mso-spacerun: yes"><FONT 
face=楷体_GB2312 size=4>&nbsp;&nbsp;&nbsp; </FONT></SPAN><FONT face=楷体_GB2312 
size=4>2)</FONT></SPAN><FONT face=楷体_GB2312 size=4><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">局部坐标系</SPAN><SPAN 
lang=EN-US>(Local Coordinate System)</SPAN><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，主要为考察物体方便起见，独立于世界坐标系来定义物体几何特性，通常是在不需要指定物体在世界坐标系中的方位的情况下，使用局部坐标系。一旦你定义“局部”物体，通过指定在局部坐标系的原点在世界坐标系中的方位，然后通过几何变换，就可很容易地将“局部”物体放入世界坐标系内，使它由局部上升为全局。</SPAN></FONT></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN style="mso-spacerun: yes"><FONT 
face=楷体_GB2312 size=4>&nbsp;&nbsp;&nbsp; </FONT></SPAN><FONT face=楷体_GB2312 
size=4>3)</FONT></SPAN><FONT face=楷体_GB2312 size=4><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">观察坐标系</SPAN><SPAN 
lang=EN-US>(Viewing coordinate systems)</SPAN><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，观察坐标系通常是以视点的位置为原点，通过用户指定的一个向上的观察向量</SPAN><SPAN 
lang=EN-US>(view up vector)</SPAN><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">来定义整个坐标系统，缺省为左手坐标系，观察坐标系主要用于从观察者的角度对整个世界坐标系内的对象进行重新定位和描述，从而简化几何物体在投影面的成像的数学推导和计算。</SPAN></FONT></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN style="mso-spacerun: yes"><FONT 
face=楷体_GB2312 size=4>&nbsp;&nbsp;&nbsp; </FONT></SPAN><FONT face=楷体_GB2312 
size=4>4)</FONT></SPAN><FONT face=楷体_GB2312 size=4><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">成像面坐标系统，它是一个二维坐标系统，主要用于指定物体在成像面上的所有点，往往是通过指定成像面与视点之间的距离来定义成像面，成像面有时也称投影面，可进一步在构影面上定义称为窗口的方形区域来实现部分成像。</SPAN></FONT></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN style="mso-spacerun: yes"><FONT 
face=楷体_GB2312 size=4>&nbsp;&nbsp;&nbsp; </FONT></SPAN><FONT face=楷体_GB2312 
size=4>5)</FONT></SPAN><FONT face=楷体_GB2312 size=4><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">屏幕坐标系统，也称设备坐标系统，它主要用于某一特殊的计算机图形显示设备</SPAN><SPAN 
lang=EN-US>(</SPAN><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">如光栅显示器</SPAN><SPAN 
lang=EN-US>)</SPAN><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">的表面的点的定义，在多数情况下，对于每一个具体的显示设备，都有一个单独的坐标系统，在定义了成像窗口的情况下，可进一步在屏幕坐标系统中定义称为视图区</SPAN><SPAN 
lang=EN-US>(view port)</SPAN><SPAN 
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">的有界区域，视图区中的成像即为实际所观察到的。</SPAN></FONT></P>
<P class=MsoNormal><SPAN lang=EN-US><FONT face=楷体_GB2312 size=4><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal><FONT face=楷体_GB2312 size=4><SPAN 
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </SPAN><SPAN 
style="mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman">总之，为在三维空间创建和显示一个</SPAN><SPAN 
lang=EN-US>(</SPAN><SPAN 
style="mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman">多个</SPAN><SPAN 
lang=EN-US>)</SPAN><SPAN 
style="mso-ascii-font-family: Times New Roman; mso-hansi-font-family: Times New Roman">几何物体，首先必须建立世界坐标系，然后，需要指定视点的方位、视线和成像面的方位，为了观察到物体的成像，还必须在各坐标系之间视见变换之后，进行投影变换，才能得到物体的成像，下面两节分别对上述坐标系之间的变换和投影变换分别加以介绍。</SPAN></FONT></P>
<P class=MsoNormal><SPAN lang=EN-US><FONT face=楷体_GB2312 size=4><![if !supportEmptyParas]><![endif]>&nbsp;<o:p></o:p></FONT></SPAN></P>
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