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COMP 175 | COMPUTER GRAPHICS

Remco Chang 1/2215 Clipping

Lecture 15:

ClippingCOMP 175: Computer GraphicsNovember 1, 2011

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Library trip

Camera assignment

problemsdebugging methods

Midterm Eval

General discussion on how we can do better

Discussions

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Last week we discussed some simple examples of clippingin Camera

We said that OpenGL takes care of a lot of that for free

But clipping is an important part of computer graphics:

Clipping

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Line Clipping

(x min , y min )

(x max , y max )

(x, y )

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Parametric Line Formulation for Clipping

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Clip Rectangle

Cohen-Sutherland Line Clipping in 2D

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If we can neither triviallyaccept or reject, then we dodivide-and-conquerSubdivide line into twosegments and test again

Cohen-Sutherland Algorithm

Cliprectangle

DC

BA

E

F

G

H

I

Use a clip edge to cut lineUse outcodes to choose which edge is crossed

The bits that are different between outcodes will tell us which edge to examinePick an order for checking edges: top bottom right left Compute the intersection point

Clip edge will be axis-aligned, so we can fix either the x or the yCan substitute into the line equation

Iterate for the newly created line segment, might need multiple passes(e.g., E-I at H)

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Cohen-Sutherland AlgorithmAlgorithm (float x0, y0, x1, y1)

ComputeOutCode(x0, y0, outcode0);ComputeOutCode(x1, y1, outcode1); repeat

check for trivial reject or trivial accept pick the point that is outside the clip rectangle

if TOP thenx = x0 + (x1 x0) * (ymax y0)/(y1 y0); y = ymax;

else if BOTTOM thenx = x0 + (x1 x0) * (ymin y0)/(y1 y0); y = ymin;

else if RIGHT theny = y0 + (y1 y0) * (xmax x0)/(x1 x0); x = xmax;

else if LEFT theny = y0 + (y1 y0) * (xmin x0)/(x1 x0); x = xmin;

if (x0, y0 is the outer point) then x0 = x; y0 = y; ComputeOutCode(x0, y0, outcode0)

else x1 = x; y1 = y; ComputeOutCode(x1, y1, outcode1)

until doneDrawRectangle(xmin, ymin, xmax, ymax) DrawLine (x0, y0, x1, y1)

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Similar to 2DDivide volume into 27 regions (picture a Rubiks cube) 6-bit outcode records results of 6 bounds tests

1 st / 2 nd bits: back & front planes3 rd / 4 th bits: top & bottom planes

5 th / 6 th bits: right & left planes

The same operation as the 2D case in using outcodes

Cohen-Sutherland Algorithm in 3D

Top plane

001000 (above)000000 (below)

Back plane

000000 (in front)100000 (behind)

Right plane

000000 (to left of)

000010 (to right of)

Bottom plane

000000 (above)

000100 (below)

Front plane

010000 (in front)000000 (behind)

Left plane

000001 (to left of)

000000 (to right of)

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Sutherland-Hodgman Polygon Clipping

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Cyrus-Beck / Liang-Barsky Parametric Line Clipping

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Parametric Line Clipping

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Parametric Line Clipping, Using Dot Product

Find t Note that if t is less than 0 or greater than 1, then theintersection occurs outside of the line segment

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Parametric Line Clipping, Solving t

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solve for t:t = N i [P 0 P E i ] / (-N i D)

Caveats: for this equation to be true, it must be

that:N i 0 (that is, the normal should not be 0; this couldoccur only as a mistake)D 0 (that is, P 1 P 0)N

i D 0 (edge E

iand line D are not parallel; if they are,

no intersection)

The algorithm needs to check for these

Parametric Line Clipping, Solving t

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When applied to line-clipping, there will be multiple t values (a t value for each clip edge test)

Eliminate t values outside of [0, 1]Determine if the intersection is considered potentiallyentering (PE) or potentially leaving (PL)

Problem, how can you tell??

Parametric Line Clipping, Against A Polygon

PE

PL

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Parametric Line Clipping, Against A Polygon

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Pre-calculate Ni and select PEi for each edge;for each line segment to be clippedif P1 = P0 then line is degenerate so clip as a point;elsebegintE = 0; tL = 1;for each candidate intersection with a clip edgeif Ni D 0 then {Ignore edges parallel to line}begincalculate t; {of line and clip edge intersection}use sign of Ni D to categorize as PE or PL; if PE then tE = max(tE,t);if PL then tL = min(tL,t);

endif tE > tL then return nilelse return P(tE) and P(tL) as true clip intersections

end

Pseudocode

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Questions?

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The intersection test can beextended to 3D

Here we try to find theintersection point (I) between aline segment (AC) and a cube

Problem is the same as the 2Done, and same or similaralgorithms can be applied

Other Types of Clipping

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Clipping works on edges of triangles (see right)

New vertices might have to becreated (e.g., points a and b)

Since clipping works with linesegments, it is similar to theCyrus-Beck algorithm, but in3D

Other Types of Clipping

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Sutherland-Hodgman Polygon Clipping

Keeps polygon info intact

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Questions?

15 clipping

Documents