三维重建笔记_投影变换_平行投影透视投影基本概念图示矩阵公式

快来打我* 2023-06-27 11:28 31阅读 0赞

**目录**

投影变换

平行投影

正投影

斜投影

透视投影 (属于中心投影)

点的透视投影

平行线段的透视变换

透视投影分类

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# 投影变换 #

根据**投影中心与投影平面（观察平面）之间的距离**（或者说，投影线是否**相交于一点**，或者说**是否保持对象的比例**），分为平行投影 和 透视投影。

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70][]

## 平行投影 ##

根据**投影方向（视线方向）****与****投影平面****的****夹角是否垂直**，平行投影可分为正平行投影（简称正投影）和斜平行投影（简称斜投影）。

### 正投影 ###

**根据****投影平面****与****坐标轴是否垂直，**正投影又可分为：三视图 和 正轴测投影。

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70 1][]

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**正轴测投影**

根据**投影平面**与**坐标轴之间的三个夹角**相等的个数（或者说**三个轴向变形系数**相等的个数），可分为正等测投影、正二测投影、正三测投影。

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70 4][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70 5][]

### 斜投影 ###

根据**投影方向与投影平面夹角a的大小**（tana=1 tana=2），斜投影可分为 **斜等侧投影** 和**斜二测投影。**

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70 6][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70 7][]

## 透视投影(属于中心投影) ##

根据**投影平面与坐标轴相交的个数**，分为一点透视，两点透视，三点透视。

透视投影属于[中心投影][Link 1]。

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70 8][]

### 点的透视投影 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70 9][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70 10][]

### 平行线段的透视变换 ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70 11][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70 12][]

### 透视投影分类 ###

一点透视，两点透视，三点透视。

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70 13][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70 14][]

**参考：**计算机图形学基础（OpenGL版）清华大学出版社 主编 徐文鹏

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[Link 1]: https://baike.baidu.com/item/%E4%B8%AD%E5%BF%83%E6%8A%95%E5%BD%B1/10524919
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