From 3e96a0ac8f6f62c8f677922ed6e9332eab422f7c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E9=99=88=E6=96=B0?= Date: Thu, 15 Apr 2021 00:42:09 +0800 Subject: [PATCH] change formula to pictures --- README.md | 95 +++++++++-------------------------------- pictures/formula1.png | Bin 0 -> 5693 bytes pictures/formula10.png | Bin 0 -> 19987 bytes pictures/formula2.png | Bin 0 -> 3979 bytes pictures/formula3.png | Bin 0 -> 2685 bytes pictures/formula4.png | Bin 0 -> 25685 bytes pictures/formula5.png | Bin 0 -> 6490 bytes pictures/formula6.png | Bin 0 -> 2358 bytes pictures/formula7.png | Bin 0 -> 16802 bytes pictures/formula8.png | Bin 0 -> 6215 bytes pictures/formula9.png | Bin 0 -> 3291 bytes 11 files changed, 19 insertions(+), 76 deletions(-) create mode 100644 pictures/formula1.png create mode 100644 pictures/formula10.png create mode 100644 pictures/formula2.png create mode 100644 pictures/formula3.png create mode 100644 pictures/formula4.png create mode 100644 pictures/formula5.png create mode 100644 pictures/formula6.png create mode 100644 pictures/formula7.png create mode 100644 pictures/formula8.png create mode 100644 pictures/formula9.png diff --git a/README.md b/README.md index f0696ba..752ea13 100644 --- a/README.md +++ b/README.md @@ -82,36 +82,25 @@ PT算法: 物体的漫反射系数$diffusionRate$、镜面反射系数$specularRate$、折射系数$refractRate$满足: -$$ -diffusionRate + specularRate + refractRate = 1 -$$ +formula1 + 对于某一条相机视线ray来说,撞击到物体也相应地将后续光线分为3部分: (1) 漫反射,在ray撞击物体点的法向半球(即上表面)随机选择一个方向反射 (2) 镜面反射,根据公式: -$$ -ReflectDir = Lx – (2 * Lx·N)*N -$$ +formula2 + 计算出反射光线的方向 (3) 透射,根据折射定律计算出折射方向 -$$ -\frac {sin \theta_1} {sin \theta_2} = \frac {n_2} {n_1} -$$ -其中,若同时具有镜面反射与折射,则采用轮盘赌的形式决定反射与折射的选择 - -$$ -\begin{aligned} -finalColor \ += \ & diffusionRate * objectColor * computePathTracing(diffuseDirection) + \\ +formula3 - & specularRate * objectColor * computePathTracing(reflectDirection) + \\ +其中,若同时具有镜面反射与折射,则采用轮盘赌的形式决定反射与折射的选择 - & refractRate* objectColor * computePathTracing(refractDirection) -\end{aligned} -$$ +formula4 主要实现在PathTracing.h和PathTracing.cpp中,也包括其余的各类object求交函数intersect等 @@ -164,27 +153,16 @@ $$ 球的uv坐标计算为: -$$ -\begin{aligned} -\phi &= atan2(z,x) \\ -\theta &= asin(y) \\ -u &= 1- \frac {\phi + \pi} {2\pi} \\ -v &= \frac {\theta + \pi / 2}{\pi} -\end{aligned} -$$ +formula5 + 见sphere.hpp的getTextureColor函数,line72-79 Bezier曲面的贴图uv坐标计算为: -$$ -\begin{aligned} -u &= \frac {\theta}{2\pi} \\ -v &= u_{bezier} -\end{aligned} -$$ - +formula6 + 贴图的图片与解释详见上文 @@ -206,54 +184,19 @@ $$ 若记xy平面内的2Dbezier参数曲线坐标与射线点坐标分别为: -$$ -P(u) = -\begin{bmatrix} -P_x(u) \\ -P_y(u) \\ -0 -\end{bmatrix} -$$ - -$$ -L(t)=rayOrigin+t*rayDirection = -\begin{bmatrix} -rayO_x + t*rayD_x \\ -rayO_y + t*rayD_y \\ -rayO_z + t*rayD_z \\ -\end{bmatrix} -$$ +formula7 绕z轴旋转$\theta$角,则曲线旋转后的点坐标为: -$$ -S(u,\theta) = -\begin{bmatrix} -P_x(u)cos\theta \\ -P_y(u) \\ --P_x(u)sin\theta -\end{bmatrix} -$$ +formula8 + 记函数: -$$ -F(t,u,\theta) = L(t) - S(u,\theta) -$$ + +formula9 + 则: -$$ -\frac {\partial F(t,u,\theta)} {\partial (t,u,\theta)} = -\begin{bmatrix} -rayD_x & -P'_x(u)cos\theta & P_x(u)sin\theta \\ -rayD_y & -P'_y(u) & 0 \\ -rayD_z & P_x(u)sin\theta & P_x(u)cos\theta \\ -\end{bmatrix} -$$ - -$$ -x(t,u,\theta) = -x(t,u,\theta) - -{\frac {\partial F(t,u,\theta)} {\partial (t,u,\theta)}}^{-1} * -F(t,u,\theta) -$$ + +formula10 最终效果如下(采样率很低的单物体图片,仅作对比使用): diff --git a/pictures/formula1.png b/pictures/formula1.png new file mode 100644 index 0000000000000000000000000000000000000000..9d148cd9d1d744734089a43de3e2fc6188fa60d8 GIT binary patch literal 5693 zcmdUT_dgq6)W24#y{aWdZK9MI9|VoPS8Q6P#BA-o)l5r_617JWv|6JmTB1sAv0_xM z5<<+HwZD13f5h{8JwM$0zUP;7&pr2?_dVynh8bzo({Rv`k&)5s>S&mfk=^7ct(B-K zNps_WU#CcL!{1a}jjRR>+#m_JTvZKK$;j%{XfGTnNHVpLj*UMV8B4(bj2jCs+#zIS zcgJ-#RLw)|whLC%wq)55i`VbD2g;?SrK^XAd7)>$AEcFNgBAMxpq~8O%WWTdbxH{IlID)sQw`g}obNoD4BX24w=up`RJ@qt|hOUs31VW{;o6P>e59>G|!p zpVXv<#Vz@ATfg|!^npKBp6_yzHcNSqsn^j2niQ~<`{U@4AKi1#a@D4bY8-6!1i 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