175 lines
3.9 KiB
Markdown
175 lines
3.9 KiB
Markdown
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---
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title: "Whitted-style光线追踪(Whitted-style Ray Tracing)"
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date: 2022-07-19T16:04:37+08:00
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---
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### 使用光线追踪的原因
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1. 光栅化无法很好地处理全局效果
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1. 软阴影
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2. 光线产生多次反弹
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2. 光栅化处理速度快但质量相对较低
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3. 光线追踪处理精准，但速度较低
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1. 光栅化：实时渲染，光线追踪：离线渲染
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2. 在生产环境中渲染一帧往往需要~10kCPU核心时
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### 光线
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1. 光线沿直线传播(虽然是错误的)
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2. 光线在相交时互不影响(虽然也是错的)
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3. 光线从光源传播到眼睛(且光路是可逆的)
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### Ray Casting
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1968年由Appel提出
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1. 通过每个像素投射一条光线的方式来生成图像
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2. 通过向光源发送光线的方式来生成阴影
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#### 生成视角射线(Generating Eye Rays)
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Pinhole Camera Model
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#### 着色像素(shading pixel)
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### 递归式光线追踪(Recursive Ray Tracing)
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Recursiv Ray Tracing 又名 Whitted-Style Ray Tracing 由T.Whitted在1980年提出
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"An improved Illumination model for shaded display"
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总体计算流程
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-------------------------------------------
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#### 射线表面相交计算(Ray-Surface Intersection)
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在进行射线表面相交计算前我们需要了解射线方程(Ray Equation)
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##### Ray Equation and Plane Equation
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射线：由一个起点和一个方向向量定义
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对应的射线方程(Ray Equation)为:
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$$r(t) = o +td , \\ \\ \\ \\ 0\leq t < 100 $$
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r：沿射线的点
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t："时间"
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o：起始点
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d：归一化后的方向向量
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-----------------
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平面：由一个法线向量和在平面上的点定义
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对应的平面方程(Plane Equation)为：
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$$P:(p - p') * N = 0,\\ \\ \\ ax+by+cz+d = 0$$
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p：所有在平面上的点
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p'：在平面上的一个点
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N：法线向量
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##### 射线与球体相交(Ray Intersection With Sphere)
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射线：$r(t) = o +td , \\ \\ \\ \\ 0\leq t < 100 $
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球体：$p:(p-c)^2 - R^2 = 0 $
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当射线与球体相交时，交点$p$必须同时满足射线和球体的方程
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此时的解为：
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$$(o + td - c )^2 - R^2 = 0$$
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##### 射线与隐式曲面相交(Ray Intersection With Implict Surface)
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射线：$r(t) = o +td , \\ \\ \\ \\ 0\leq t < 100 $
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一般隐式曲面：$p:f(p) = 0$
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代入后的替代射线方程：$f(o + td) = 0$
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！解必须为正根
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##### 射线与三角形网格相交(Ray Intersection With Triangle Mesh)
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原因：
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1. 渲染上：计算可见性，阴影，光照
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2. 几何上：判断内外关系
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计算：拆分
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1. 最简单的方式：对每个三角形进行一次相交判断
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2. 最简单但速度最慢
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3. 可以出现0次相交或一次相交
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##### 射线与三角形相交(Ray Intersection With Triangle)
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三角形可以视为在一个平面中
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1. 可视为射线与平面相交
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2. 判断相交点是否位于三角形内部即可
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##### 射线与平面相交(Ray Intersection With Plane)
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射线方程：$r(t) = o +td , \\ \\ \\ \\ 0\leq t < 100 $
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平面方程：$P:(p - p') * N = 0,\\ \\ \\ ax+by+cz+d = 0$
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相交的解为：
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设$p = r(t)$求解$t(0\leq t < \infty)$
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$(p-p') * N = (o + td - p') * N = 0$
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$t = \frac{(p'-o) * N }{d * N}$
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##### Möller Trumbore Algorithm
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一种更快地得出重心坐标的算法
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### 光线追踪的性能瓶颈
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通过简单地计算光线与场景的相交的方式：
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1. 需要对场景中每一个三角形判断光线是否相交
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2. 找到最接近的交点(即最小的t值)
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带来的问题：
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1. 算法复杂度 = $pixels \times triangles (\times bounces)$
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2. 计算耗时极高
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解决办法：
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1. 采取遍历物体而非三角形的方式进行计算
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2. 采用相关加速结构/算法
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---------------------------------------
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