Rendering

Concepts Geometry Optics 光的直线传播定律 光的反射定律 法向量：$N$ 入射光：$L$ （归一化） 反射光：$R=2(N\cdot L)N L$ 光的折射定律 Snell's law: $\eta L\sin\theta L=\eta T\sin\theta T$ $T= N\sqrt{1 \frac{\eta^2 L}{\eta^...

Rendering Rendering: The process of generating an image from a model, by means of a computer program Model Rendering Image Display image + model comp = painting, photography model...

Introduction Good at simulating specular effects Rays are reflected, refracted or absorbed 三角形法向：$N=\frac{(P 1 P 0)\times(P 2 P 0)}{\|(P 1 P 0)\times(P 2 P 0)\|}$ 计算每个顶点法向：$N v=\fr...

Introduction Why Transformation Modeling Moving the objects to the desired location Multiple instances of a protostype stape Kinematics of linkages/skeletons character animation Vi...

数值积分 Limitation 对于 $d$ 维函数 $f$，一维情况下 $O(n^{ r})$ 收敛，则高维仅 $O(n^{ \frac{r}{s}})$ 收敛 不连续：$O(n^{ \frac{r}{s}})$ Monte Carlo Method: $\int 0^1f(x)dx =\frac{1}{N}\sum {i=1}^Nf(x i)$ Adav...

pinhole camera near plane far plane NDC: normalized device coordinate space 从 (0,0,0) 到 (1,1,1) 设备无关 Raster space: NDC 乘以分辨率 look at Transformation Orthographic projection Perspect...

Math Fourier Series: 任意周期为 $1$ 的函数可表示为 $\frac{a 0}{2}+\sum {n=1}^N(a n\cos(2\pi nt)+b n\sin(2\pi nt))$ $f(x)=\sum {n= N}^Nc ne^{2\pi int},c n=\int 0^1e^{ 2\pi int}f(t)dt$ $(f g)(t)...