Scene Graphs
COMP 575 / COMP 770
1
Scene Graphs
Good background at Wikipedia:
http:/en.wikipedia.org/wiki/Scene_graph
1. A scene graph is a collection of nodes in a graph or tree
structure
2. Nodes in a scene graph (generally) represent entities or
objec
Comp 575/770 Midterm Answers 6-9
Michael Coleman
March 28, 2013
6.1
1. Translation and Translation? True
2. Translation and Scale? False
3. Translation and Rotation? False
4. Scale and Rotation? False
5. Rotation and Rotation? False
6.2 Write a sequence o
Ray Tracing
Dinesh Manocha
COMP 575/770
Overview
Review
Ray Tracing flavors
Recursive ray tracing
Distributed ray tracing
Ray Tracing vs. rasterization
Overview
Review
Ray Tracing flavors
Recursive ray tracing
Distributed ray tracing
Ray Tracing
Pipeline Operations
COMP575/COMP770 Spring 2016
1
Pipeline
overview
you are here
3D transformations; shading
conversion of primitives to pixels
blending, compositing, shading
user sees this
APPLICATION
COMMAND STREAM
VERTEX PROCESSING
TRANSFORMED GEOMETRY
Ray Tracing, Part 1
Dinesh Manocha
COMP 575/770
Overview
Acceleration structures
Spatial hierarchies
Object hierarchies
Interactive Ray Tracing techniques
Optimized hierarchy construction
Optimized hierarchy traversal - Ray
packets
Last lecture
Ray
Ray Tracing, Part 1
Dinesh Manocha
COMP 575/770
Overview
Acceleration structures
Spatial hierarchies
Object hierarchies
Interactive Ray Tracing techniques
Optimized hierarchy construction
Optimized hierarchy traversal - Ray packets
Last lecture
Ray
Midterm Solutions
April 1, 2016
1
a1
) + Imin
255
a2
= Imax (
) + Imin
255
I1 = Imax (
(1)
I2
(2)
Subtracting the two equations,
a1 a2
255
(I1 I2 )255
=
a1 a2
I1 I2 = Imax
Imax
(3)
(4)
Put the value of Imax in the original equations to get the value of
Color Theory
COMP575/COMP770
Today:
Finish up Color
Tone mapping
Image representation
Color Theory
CIE XYZ color space
3 color matching functions: X, Y, Z
Y is luminance
X and Z are color values
WP user acdx
Color Theory
xyY color space
Since Y is luminan
Color Theory
COMP575/COMP770
Dinesh Manocha
Overview
Welcome!
Today:
Color representation
Video hardware
Gamma
Color theory
Homework
Color representation
How to store colors in the computer?
Color representation
Grays
How many colors are there?
How many b
3D Viewing
COMP 770
Fall 2011
1
Viewing, backward and forward
So far have used the backward approach to viewing
start from pixel
ask what part of scene projects to pixel
explicitly construct the ray corresponding to the pixel
Next will look
Spline Curves
COMP 575/COMP 770
1
Motivation: smoothness
In many applications we need smooth
shapes
[Boeing]
that is, without discontinuities
So far we can make
things with corners (lines, squares, rectangles, )
circles and ellipses (only get you so
Pipeline and Rasterization
COMP575/COMP770
Spring 2016
1
The graphics pipeline
The standard approach to object-order graphics
Many versions exist
software, e.g. Pixars REYES architecture
many options for quality and flexibility
hardware, e.g. graphic
2D Geometric Transformations
COMP 575/770
Spring 2016
1
A little quick math background
Notation for sets, functions, mappings
Linear transformations
Matrices
Matrix-vector multiplication
Matrix-matrix multiplication
Geometry of curves in 2D
Implici
Sampling and reconstruction
COMP 575/COMP 770
Spring 2016
1
Sampled representations
How to store and compute with continuous functions?
Common scheme for representation: samples
[FvDFH fig.14.14b / Wolberg]
write down the functions values at many points
3D Transformations
COMP 770
Fall 2011
Translation
Scaling
Rotation about z axis
Rotation about x axis
Rotation about y axis
General rotations
A rotation in 2D is around a point
A rotation in 3D is around an axis
so 3D rotation is w.r.t a lin
Images and Displays
COMP575/770 Lecture 2
1
What is an image?
A photographic print
A photographic negative?
This projection screen
Some numbers in RAM?
2
An image is:
A 2D distribution of intensity or color
A function defined on a two-dimensional pl
Ray Tracing
COMP575/COMP770
1
Ray tracing idea
2
Ray Tracing: Example
(from [Whitted80])
Ray Tracing: Example
Ray Tracing for Highly Realistic
Images
Volkswagen Beetle with correct shadows and (multi-)reflections on
curved surfaces
Reasons
Spline Curves
COMP 575/COMP 770
1
Motivation: smoothness
In many applications we need smooth shapes
[Boeing]
that is, without discontinuities
So far we can make
things with corners (lines, squares, rectangles, )
circles and ellipses (only get you so
Perspective
COMP575/COMP770
January 23, 2013
1
History of projection
Ancient times: Greeks wrote about laws of
perspective
Renaissance: perspective is adopted by artists
Duccio c. 1308
2
History of projection
Later Renaissance: perspective
Triangle meshes
COMP575/COMP 770
1
Notation
nT = #tris; nV = #verts; nE = #edges
Euler: nV nE + nT = 2 for a simple closed surface
and in general sums to small integer
[Foley et al.]
argument for implication that nT:nE:nV is about 2:3:1
2
Validity of
Visibility Computations
Visible Surface Determination
Global Visibility Computations
Visibility Culling
COMP 575/COMP770:
Dinesh Manocha,
Visible Surface Determination
Given a set of 3D objects and a viewing
specification, determine the lines or
surfac
Images and Displays
COMP575/770 Lecture 2
1
What is an image?
A photographic print
A photographic negative?
This projection screen
Some numbers in RAM?
2
An image is:
A 2D distribution of intensity or color
A function defined on a two-dimensional pl