Clipping II, Hidden Surfaces I Week 8, Fri Mar 9 - - PowerPoint PPT Presentation

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Clipping II, Hidden Surfaces I Week 8, Fri Mar 9 - - PowerPoint PPT Presentation

Apr 09, 2023 248 likes •868 views

University of British Columbia CPSC 314 Computer Graphics Jan-Apr 2007 Tamara Munzner Clipping II, Hidden Surfaces I Week 8, Fri Mar 9 http://www.ugrad.cs.ubc.ca/~cs314/Vjan2007 Reading for This Time FCG Chap 12 Graphics Pipeline

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SLIDE 1

University of British Columbia CPSC 314 Computer Graphics Jan-Apr 2007 Tamara Munzner http://www.ugrad.cs.ubc.ca/~cs314/Vjan2007

Clipping II, Hidden Surfaces I Week 8, Fri Mar 9

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2

Reading for This Time

  • FCG Chap 12 Graphics Pipeline
  • only 12.1-12.4
  • FCG Chap 8 Hidden Surfaces
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SLIDE 3

3

News

  • Project 3 update
  • Linux executable reposted
  • template update
  • download package again OR
  • just change line 31 of src/main.cpp from

int resolution[2]; to int resolution[] = {100,100}; OR

  • implement resolution parsing
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SLIDE 4

4

Review: Clipping

  • analytically calculating the portions of

primitives within the viewport

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5

Review: Clipping Lines To Viewport

  • combining trivial accepts/rejects
  • trivially accept lines with both endpoints inside all edges
  • f the viewport
  • trivially reject lines with both endpoints outside the same

edge of the viewport

  • otherwise, reduce to trivial cases by splitting into two

segments

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SLIDE 6

6

Review: Cohen-Sutherland Line Clipping

  • outcodes
  • 4 flags encoding position of a point relative to

top, bottom, left, and right boundary

x= x=x xmin

min

x= x=x xmax

max

y= y=y ymin

min

y= y=y ymax

max

0000 0000 1010 1010 1000 1000 1001 1001 0010 0010 0001 0001 0110 0110 0100 0100 0101 0101 p1 p1 p2 p2 p3 p3

  • OC(p1)== 0 &&

OC(p2)==0

  • trivial accept
  • (OC(p1) &

OC(p2))!= 0

  • trivial reject
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7

Clipping II

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8

Polygon Clipping

  • objective
  • 2D: clip polygon against rectangular window
  • or general convex polygons
  • extensions for non-convex or general polygons
  • 3D: clip polygon against parallelpiped
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9

Polygon Clipping

  • not just clipping all boundary lines
  • may have to introduce new line segments
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10

  • what happens to a triangle during clipping?
  • some possible outcomes:
  • how many sides can result from a triangle?
  • seven

triangle to triangle

Why Is Clipping Hard?

triangle to quad triangle to 5-gon

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11

  • a really tough case:

Why Is Clipping Hard?

concave polygon to multiple polygons

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12

Polygon Clipping

  • classes of polygons
  • triangles
  • convex
  • concave
  • holes and self-intersection
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SLIDE 13

13

Sutherland-Hodgeman Clipping

  • basic idea:
  • consider each edge of the viewport individually
  • clip the polygon against the edge equation
  • after doing all edges, the polygon is fully clipped
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SLIDE 14

14

Sutherland-Hodgeman Clipping

  • basic idea:
  • consider each edge of the viewport individually
  • clip the polygon against the edge equation
  • after doing all edges, the polygon is fully clipped
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SLIDE 15

15

Sutherland-Hodgeman Clipping

  • basic idea:
  • consider each edge of the viewport individually
  • clip the polygon against the edge equation
  • after doing all edges, the polygon is fully clipped
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SLIDE 16

16

Sutherland-Hodgeman Clipping

  • basic idea:
  • consider each edge of the viewport individually
  • clip the polygon against the edge equation
  • after doing all edges, the polygon is fully clipped
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SLIDE 17

17

Sutherland-Hodgeman Clipping

  • basic idea:
  • consider each edge of the viewport individually
  • clip the polygon against the edge equation
  • after doing all edges, the polygon is fully clipped
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SLIDE 18

18

Sutherland-Hodgeman Clipping

  • basic idea:
  • consider each edge of the viewport individually
  • clip the polygon against the edge equation
  • after doing all edges, the polygon is fully clipped
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SLIDE 19

19

Sutherland-Hodgeman Clipping

  • basic idea:
  • consider each edge of the viewport individually
  • clip the polygon against the edge equation
  • after doing all edges, the polygon is fully clipped
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SLIDE 20

20

Sutherland-Hodgeman Clipping

  • basic idea:
  • consider each edge of the viewport individually
  • clip the polygon against the edge equation
  • after doing all edges, the polygon is fully clipped
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21

Sutherland-Hodgeman Clipping

  • basic idea:
  • consider each edge of the viewport individually
  • clip the polygon against the edge equation
  • after doing all edges, the polygon is fully clipped
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22

Sutherland-Hodgeman Algorithm

  • input/output for whole algorithm
  • input: list of polygon vertices in order
  • output: list of clipped polygon vertices consisting of
  • ld vertices (maybe) and new vertices (maybe)
  • input/output for each step
  • input: list of vertices
  • output: list of vertices, possibly with changes
  • basic routine
  • go around polygon one vertex at a time
  • decide what to do based on 4 possibilities
  • is vertex inside or outside?
  • is previous vertex inside or outside?
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23

Clipping Against One Edge

  • p[i] inside: 2 cases
  • utside
  • utside

inside inside inside inside

  • utside
  • utside

p[i] p[i] p[i-1] p[i-1]

  • utput:
  • utput: p[i]

p[i] p[i] p[i] p[i-1] p[i-1] p p

  • utput:
  • utput: p,

p, p[i] p[i]

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24

Clipping Against One Edge

  • p[i] outside: 2 cases

p[i] p[i] p[i-1] p[i-1]

  • utput:
  • utput: p

p p[i] p[i] p[i-1] p[i-1] p p

  • utput: nothing
  • utput: nothing
  • utside
  • utside

inside inside inside inside

  • utside
  • utside
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Clipping Against One Edge

clipPolygonToEdge( p[n], edge ) { for( i= 0 ; i< n ; i++ ) { if( p[i] inside edge ) { if( p[i-1] inside edge ) output p[i]; // p[-1]= p[n-1] else { p= intersect( p[i-1], p[i], edge ); output p, p[i]; } } else { // p[i] is outside edge if( p[i-1] inside edge ) { p= intersect(p[i-1], p[I], edge ); output p; } } }

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26

Sutherland-Hodgeman Example

inside inside

  • utside
  • utside

p0 p0 p1 p1 p2 p2 p3 p3 p4 p4 p5 p5 p7 p7 p6 p6

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Sutherland-Hodgeman Discussion

  • similar to Cohen/Sutherland line clipping
  • inside/outside tests: outcodes
  • intersection of line segment with edge:

window-edge coordinates

  • clipping against individual edges independent
  • great for hardware (pipelining)
  • all vertices required in memory at same time
  • not so good, but unavoidable
  • another reason for using triangles only in

hardware rendering

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28

Hidden Surface Removal

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Occlusion

  • for most interesting scenes, some polygons
  • verlap
  • to render the correct image, we need to

determine which polygons occlude which

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30

Painter’s Algorithm

  • simple: render the polygons from back to

front, “painting over” previous polygons

  • draw blue, then green, then orange
  • will this work in the general case?
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Painter’s Algorithm: Problems

  • intersecting polygons present a problem
  • even non-intersecting polygons can form a

cycle with no valid visibility order:

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Analytic Visibility Algorithms

  • early visibility algorithms computed the set of visible

polygon fragments directly, then rendered the fragments to a display:

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Analytic Visibility Algorithms

  • what is the minimum worst-case cost of

computing the fragments for a scene composed of n polygons?

  • answer:

O(n2)

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34

Analytic Visibility Algorithms

  • so, for about a decade (late 60s to late 70s)

there was intense interest in finding efficient algorithms for hidden surface removal

  • we’ll talk about one:
  • Binary Space Partition (BSP) Trees
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35

Binary Space Partition Trees (1979)

  • BSP Tree: partition space with binary tree of

planes

  • idea: divide space recursively into half-spaces

by choosing splitting planes that separate

  • bjects in scene
  • preprocessing: create binary tree of planes
  • runtime: correctly traversing this tree

enumerates objects from back to front

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36

Creating BSP Trees: Objects

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Creating BSP Trees: Objects

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Creating BSP Trees: Objects

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39

Creating BSP Trees: Objects

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Creating BSP Trees: Objects

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Splitting Objects

  • no bunnies were harmed in previous

example

  • but what if a splitting plane passes through

an object?

  • split the object; give half to each node

Ouch

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42

Traversing BSP Trees

  • tree creation independent of viewpoint
  • preprocessing step
  • tree traversal uses viewpoint
  • runtime, happens for many different viewpoints
  • each plane divides world into near and far
  • for given viewpoint, decide which side is near and

which is far

  • check which side of plane viewpoint is on

independently for each tree vertex

  • tree traversal differs depending on viewpoint!
  • recursive algorithm
  • recurse on far side
  • draw object
  • recurse on near side
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43

Traversing BSP Trees

renderBSP(BSPtree *T) BSPtree *near, *far; if (eye on left side of T->plane) near = T->left; far = T->right; else near = T->right; far = T->left; renderBSP(far); if (T is a leaf node) renderObject(T) renderBSP(near); query: given a viewpoint, produce an ordered list of (possibly split) objects from back to front:

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BSP Trees : Viewpoint A

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BSP Trees : Viewpoint A

F N F N

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BSP Trees : Viewpoint A

F N F N F N

ν decide independently at

each tree vertex

ν not just left or right child!

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BSP Trees : Viewpoint A

F N F N N F F N

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BSP Trees : Viewpoint A

F N F N N F F N

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BSP Trees : Viewpoint A

F N F N F N N F 1 1

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BSP Trees : Viewpoint A

F N F N F N F N N F 1 2 1 2

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BSP Trees : Viewpoint A

F N F N F N F N N F N F 1 2 1 2

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BSP Trees : Viewpoint A

F N F N F N F N N F N F 1 2 1 2

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BSP Trees : Viewpoint A

F N F N F N F N N F N F 1 2 3 1 2 3

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BSP Trees : Viewpoint A

F N F N F N N F N F 1 2 3 4 F N 1 2 3 4

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BSP Trees : Viewpoint A

F N F N F N N F N F 1 2 3 4 5 F N 1 2 3 4 5

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BSP Trees : Viewpoint A

F N F N F N N F N F 1 2 3 4 5 1 2 3 4 5 6 7 8 9 6 7 8 9 F N F N F N

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BSP Trees : Viewpoint B

N F F N F N F N F N F N F N N F

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BSP Trees : Viewpoint B

N F F N F N F N 1 3 4 2 F N F N F N N F 5 6 7 8 9 1 2 3 4 5 6 7 9 8

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BSP Tree Traversal: Polygons

  • split along the plane defined by any polygon

from scene

  • classify all polygons into positive or negative

half-space of the plane

  • if a polygon intersects plane, split polygon into

two and classify them both

  • recurse down the negative half-space
  • recurse down the positive half-space
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BSP Demo

  • useful demo:

http://symbolcraft.com/graphics/bsp

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Summary: BSP Trees

  • pros:
  • simple, elegant scheme
  • correct version of painter’s algorithm back-to-front

rendering approach

  • was very popular for video games (but getting less so)
  • cons:
  • slow to construct tree: O(n log n) to split, sort
  • splitting increases polygon count: O(n2) worst-case
  • computationally intense preprocessing stage restricts

algorithm to static scenes