Advanced Computer Graphics: Difference between revisions

← Older edit

@@ Line 1: / Line 1: @@
-Classnotes for CMSC740 taught by Matthias Zwicker
+Classnotes for CMSC740 taught by Matthias Zwicker (Spring 2020).<br>
+This first portion of the class focuses on ray tracing (specifically, path tracing) and is based on the [https://www.pbrt.org/ PBRT book]<br>
+The second portion of the class introduces deep learning approaches to computer graphics.
 ==Acceleration==
@@ Line 101: / Line 103: @@
 ===Bidirectional Path Tracing===
 Trace path from eye and light<br>
-E.g from eye we get path <math>z_0, z_1, z_2</math><br>
+Example:
-from light we get <math>y_0, y_1</math><br>
+* from eye we get path <math>z_0, z_1, z_2</math><br>
-Then make shadow rays from every pair of z, y<br>
+* from light we get <math>y_0, y_1</math><br>
+* Then make shadow rays from every pair of z, y<br>
-==Ignore==
+Path of length k with k+1 vertices
-[[Visible to::users]]
+* s vertices from light, t from eye
+* Path denoted <math>\bar{X}^{s,t}</math> (e.g. <math>\bar{X}^{2,3}</math>)
+* We also get probability density for this path <math>p_{s,t}</math>
+==Participating Media==
+===Transmittance===
+* Multiplicative property
+** <math>T(s)=T(s_0) * T(s_1)</math>
+* Beer's law <math>T(s)=e^{-sigma_t s}</math>
+** For homogenous media where <math>\sigma(x) = \sigma</math> is constant
+===Phase Functions===
+====Henyey-Greenstein phase function====
+* <math>p(\cos \theta) = \frac{1-g^2}{4\pi(1+g^2-2g\cos \theta)^{1.5}}</math>
+====Properties====
+* Unitless
+* Reciprocity
+** <math>p(\omega' \rightarrow \omega) = p(\omega \rightarrow \omega')</math>
+* Energy conservation
+** Integrates to 1
+* Average phase angle determined by g
+===Volume Rendering Equation===
+====Integro-integral form====
+* <math>L(\mathbf{x}, \omega) = \int_{0}^{\infty}\exp(-\int_{0}^{s'}\sigma_t(\mathbf{x}-s''\omega)ds'')S(\mathbf{x}-s'\omega, \omega)ds</math>
+** <math>\exp(-\int_{0}^{s'}\sigma_t(\mathbf{x}-s''\omega)ds'')</math> is Transmittance <math>T(s')</math> due to extinction
+** <math>S(\mathbf{x}-s'\omega, \omega)</math> is source (emission, in-scattering)
+===Subsurface Scattering===
+====BSSRDF====
+bidirectional surface scattering reflectance distribution function
+* <math>S(\mathbf{x}_i, \omega_i, \mathbf{x}_o, \omega_o)</math>
+==Surface Reconstruction==
+===Crust Technique===
+[https://www.cs.ubc.ca/~sheffa/dgp/ppts/crust.pdf Crust Slides from Univ. BC]