David Luebke10/9/2015 CS 551 / 645: Introductory Computer Graphics David Luebke [email protected] cs551

David Luebke 04/21/23

CS 551 / 645: Introductory Computer Graphics

David Luebke

[email protected]

http://www.cs.virginia.edu/~cs551


Administrivia

Upcoming graphics events– Graphics lunch: Olsson 236D

Ongoing, informal event; bring your lunch

– “Graphics week”: 2 upcoming colloquia Dec 1: Dan Aliaga (Bell Labs), Image-Based Rendering Dec 6: Ben Watson (U. Alberta), Level of detail control


Recap: Ray Casting

An example:

ScreenEyepoint Scene


Recap: Recursive Ray Tracing

Obvious extension: – Spawn additional rays off reflective surfaces– Spawn transmitted rays through transparent

surfaces

Leads to recursive ray tracing

Primary Ray

Secondary Rays


Recap: Basic Algorithm

Object allObs[];

Color image[];

RayTraceScene()

allObs = initObjects();

for (Y all rows in image)for (X all pixels in row) Ray R = calcPrimaryRay(X,Y);

image[X,Y] = TraceRay(R);display(image);


Recap: Basic Algorithm

Color TraceRay(Ray R)

if rayHitsObjects(R) then

Color localC, reflectC, refractC;

Object O = findNearestObject(R);

localC = shade(O,R);

Ray reflectedRay = calcReflect(O,R)

Ray refractedRay = calcRefract(O,R)

reflectC = TraceRay(reflectedRay);

refractC = TraceRay(refractedRay);

return localC reflectC refractCelse return backgroundColor


Recap: Representing Rays

We represent a ray parametrically: – A starting point O– A direction vector D– A scalar t

O

D

t = 1t < 0

R = O + tDt > 1


Recap: Ray-Polygon Intersection

Find plane equation of polygon:ax + by + cz + d = 0

To find coefficients:N = [a, b, c]

d = N P1

x

yN

P1

P2

d


Recap: Ray-Polygon Intersection

Find intersection of ray and plane:t = -(aOx + bOy + cOz + d) / (aDx + bDy + cDz)

Does polygon contain intersection point Pi ?– One simple algorithm:

Draw line from Pi to each polygon vertex Measure angles between lines (how?) If sum of angles between lines is 360°,

polygon contains Pi

– Slow — better algorithms available


Recap: Shadow Rays

Simple idea: – Where a ray intersects a surface, send a shadow

ray to each light source– If the shadow ray hits any surface before the light

source, ignore light

Note: each ray-surface intersection now spawns n + 2 rays, n = # light sources– Remember: intersections 95% of work


Recap: Shadow Rays

Some problems with using shadow rays as described: – Lots of computation– Infinitely sharp shadows– No semitransparent object shadows


Shadow Ray Problems:Too Much Computation Light buffer (Haines/Greenberg, 86)

– Precompute lists of polygons surrounding light source in all directions

– Sort each list by distance to light source– Now shadow ray need only be intersected with appropriate

list!

Occluding Polys

ShadowRay

Current Intersection Point

Light Buffer


Shadow Rays



Shadow Ray Problems:Sharp Shadows Why are the shadows sharp? A: Infinitely small point light sources What can we do about it? A: Implement area light sources How?


Shadow Ray Problems: Area Light Sources

30% blockage

Could trace a conical beam from point of intersection to light source:

Track portion of beam blocked by occluding polygons:


Shadow Ray Problems:Area Light Sources Too hard! Approximate instead: Sample the light source over its area and

take weighted average:

50% blockage


Shadow Ray Problems:Area Light Sources Disadvantages:

– Less accurate (50% vs. 30% blockage)– Oops! Just quadrupled (at least) number of

shadow rays

Moral of the story: – Soft shadows are very expensive in ray tracing


Shadow Rays



Shadow Ray Problems:Semitransparent Objects In principle:

– Translucent colored objects should cast colored shadows

– Translucent curved objects should create refractive caustics

In practice:– Can fake colored shadows by attenuating color

with distance– Caustics need backward ray tracing


Speedup Techniques

Intersect rays faster Shoot fewer rays Shoot “smarter” rays


Speedup Techniques

Intersect rays faster Shoot fewer rays Shoot “smarter” rays


Intersect Rays Faster

Bounding volumes Spatial partitions Reordering ray intersection tests Optimizing intersection tests


Bounding Volumes

Bounding volumes– Idea: before intersecting a ray with a collection of

objects, test it against one simple object that bounds the collection

0

1

2

3

4

56

78

90

1

2

3

4

56

78

9


Bounding Volumes

Hierarchical bounding volumes– Group nearby volumes hierarchically– Test rays against hierarchy top-down


Bounding Volumes

Different bounding volumes – Spheres

Cheap intersection test Poor fit Tough to calculate optimal clustering

– Axis-aligned bounding boxes (AABBs) Relatively cheap intersection test Usually better fit Trivial to calculate clustering


Bounding Volumes

More bounding volumes– Oriented bounding boxes (OBBs)

Medium-expensive intersection test Very good fit (asymptotically better) Medium-difficult to calculate clustering

– Slabs (parallel planes) Comparatively expensive Very good fit Difficult to calculate good clustering


Spatial Partitioning

Hierarchical bounding volumes surround objects in the scene with (possibly overlapping) volumes

Spatial partitioning techniques classify all space into non-overlapping portions


Spatial Partitioning

Example spatial partitions:– Uniform grid (2-D or 3-D)– Octree– k-D tree– BSP-tree


Uniform Grid

Uniform grid pros:– Very simple and fast to generate– Very simple and fast to trace rays across (How?)

Uniform grid cons:– Not adaptive

Wastes storage on empty space Assumes uniform spread of data


Octree

Octree pros:– Simple to generate– Adaptive

Octree cons:– Nontrivial to trace rays across– Adaptive only in scale


k-D Trees

k-D tree pros:– Moderately simple to generate– More adaptive than octrees

k-D tree cons:– Less efficient to trace rays across– Moderately complex data structure


BSP Trees

BSP tree pros:– Extremely adaptive– Simple & elegant data structure

BSP tree cons:– Very hard to create optimum BSP– Splitting planes can explode storage– Simple but slow to trace rays across


Reordering RayIntersection Tests Caching ray hits (esp. shadow rays) Memory-coherent ray tracing


Optimizing Ray Intersection Tests Fine-tune the math!

– Share subexpressions– Precompute everything possible

Code with care– Even use assembly, if necessary

Documents

David Luebke10/9/2015 CS 551 / 645: Introductory Computer Graphics David Luebke [email protected] cs551