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91 lines
1.9 KiB
Markdown
91 lines
1.9 KiB
Markdown
+++
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author = "Wxn"
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title = "三维方向的思考"
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date = "2023-11-05"
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description = "Please read me first."
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tags = [
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"三维方向的思考",
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]
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categories = [
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"个人随笔",
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]
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+++
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This article offers a sample of basic Markdown.
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<!--more-->
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# 正文开始
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## OpenGL
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着色器与纹理贴图
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## 一道题
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如何判断一个点(x,y)在一个多边形的内部,外部,还是边上?
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我们先来看看国外教授的看法:https://alienryderflex.com/polygon/
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这种情况有点特殊,而且如果遇到了也不知道如何解决.所以我找找看有没有更简单的办法
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----
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下面这个同学讲的很好,使用叉乘!
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博客:【如何判断点在多边形内部 - CSDN App】http://t.csdnimg.cn/JMdc7
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视频:[教学视频](https://www.bilibili.com/video/BV1FD4y1i7Dy/?share_source=copy_web&vd_source=9a022d27a757e495adc6e15743c4ec1d)
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<font color=red>下面来讲一下叉乘</font>:这个很重要:<font color=orange>右手定则,叉乘结果的方向,叉乘a与b的先后顺序</font>
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### 叉乘:
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a（x1，y1），b（x2，y2），则a×b=（x1\*y2-x2\*y1）
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---
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```
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顶点一:(0,0,0)
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顶点二:(1,0,0)
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顶点三:(0,1,0)
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向量a = (1,0,0)-(0,0,0) = (1,0,0) = (a₁,a₂,a₃)
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向量b = (0,1,0)-(0,0,0) = (0,1,0) = (b₁,b₂,b₃)
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axb = (0,0,1)
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```
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至于为啥 (1,0,0) $X$ (0,1,0) = (0,0,1)?
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根据叉积的计算公式为：==23 32, 31 13,12 21==
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$a × b$ = ($a₂b₃$- $a₃b₂$, $a₃b₁$ - $a₁b₃$, $a₁b₂$ - $a₂b₁$)
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=(0\*0-0\*1, 0\*0-1\*0, 1\*1-0\*0)
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=(0, 0 ,1)
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### 点乘:(完整)
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上面是二维,下面是三维:
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V1( x1, y1, z1)·V2(x2, y2, z2) = x1\*x2 + y1\*y2 + z1\*z2
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## 继续这道题
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## 四元数又是什么?
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