“加油阿考”
打开了熟悉的CSE160，怀念艰难又快乐的画树时光。大学至此，没有比在加州更好的日子了。
参考书：Angel & Shreiner: Online examples
Lighting & Shading
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vertex shader and fragment shader
vertex: describe vertices’ features, like position and color
fragment: fragment is like a pixel, a unit of an image
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ambient, diffuse and specular lighting
ambient: the light that is already present in a scene, before any additional lighting is added
diffuse: scattered and comes from all directions
specular: identifies the bright specular highlights that occur when light hits an object surface and reflects back toward the camera
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flat shading, gouraud shading and phong shading
flat: all of the polygons reflect as a flat surface, giving a blocky look and feel to a model
gouraud: smooth shading, per-vertex, vertex shader get color passed to fragment shader
phong: smooth shading, per-fragment, vertex shader passed position and normal to fragment shader
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formula
$I_d = IK_dcos\theta$
$I_a = IK_a$
$I_s = IK_scos^n\alpha$
$\vec H = \vec L + \vec V$
$\hat R = 2\hat N(\hat N \cdot\vec L)-\vec L$
$I_4 = \frac{y_4-y_2}{y_1-y_2}I_1+\frac{y_1-y_4}{y_1-y_2}I_2$
$I_p = \frac{x_5-x_p}{x_5-x_4}I_4+\frac{x_p-x_4}{x_5-x_4}I_5$
$I$: light color, 1 * 3 vector, rgb
$\theta$: angle between lighting and normal
$\alpha$: angle between reflection light and view
$n$: glosiness factor; the larger it is, the brighter and smaller the reflective point will be
$\hat H$: half vector of light direction and view direction
$\hat R$: based on light direction and normal, calculate reflective light’s direction
last two lines: linear interpolation for gouraud shading
Parametric Curves
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linear, quadratic and cubic
Example: Given 3 pts, $p_0, p_1, p_2$
$p(t)=at^2+bt+1=[t^2, t, 1]MG$
$G=[p0, p1, p2]^T$
linear: 2pts
quadratic: 3 pts
cubic: 4 pts
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interpolation
Example: solve $c$ in $p(u)=u^Tc$, such that $p(u)$ interpolates the given 4 pts
$p_0=p(0)=c_0$
$p_1=p(\frac{1}{3})=c_0+\frac{1}{3}c_1+(\frac{1}{3})^2c_2+(\frac{1}{3})^3c_3$
$p_2=p(\frac{2}{3})=c_0+\frac{2}{3}c_1+(\frac{2}{3})^2c_2+(\frac{2}{3})^3c_3$
$p_3=p(1)=c_0+c_1+c_2+c_3$
Write the above functions as below:
$p=Ac$, where $p=[p0, p1, p2, p3]^T$
and $A$ is a matrix containing all the coefficients
can calculate inverse matrix of $A$ to get $c$
suppose $M = A^{-1}$, then $c=Mp$
interpolation can also be used in bicubic surface patch
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blending function
$p(u)=u^Tc=u^TMp=b(u)^Tp$
where $b(u)=M^Tu=[b_0(u), b_1(u), b_2(u), b_3(u)]^T$
$p(u)=b_0(u)p_0+b_1(u)p_1+b_2(u)p_2+b_3(u)p_3=\sum^3_{i=0}b_i(u)p_i$
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Hermite, Bezier, B-Splines
they are 3 types of curves with different $M$
Hermite: suppose we have $p_0$ and $p_3$, and the derivative value at $u=0$ and $u=1$, need to solve difference control point at $u=0$ and $u=1$
$M_H=$
Bezier: use 4 pts again, but 2 of them control the derivative values at $u=0$ and $u=1$
$M_B=$
B-Splines: I can’t understand
$M_S=\frac{1}{6}$
