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Tong-Yee Lee

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2D/3D Polygon Clipping

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A view frustum, with near- and far- clip planes. Only the shaded volume is rendered.

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  • 2D Clipping but waste division for outside viewing window
  • We have better clip model before division by w

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This manner is OK. But, it needs “Division” before clipping.

Sometimes, it is kind of waste.

​

For example, red color shapes below.

Z = -n

Z=-f

Z=0

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Another Trivial Rejection Clipping

w = -z

What does it imply?

Remember if a point is behind eye, we can not

see it!!. i.e., z > 0, means it is behind eye.

So, we can check the fourth item (before division).

If the fourth item is negative, this point is behind

the eye point.

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Removing Back-Faces

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  • Idea: Compare the normal of each face with the viewing direction ��Given n, the outward-pointing normal of F ��for each face F of object �    if (n . v > 0) �        throw away the face��Does it work?

It always culls half

number of input polygons

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A

B

P: output

Inside

Outside

Case 1

A

B

Inside

Outside

P’: output

Case 2

A

B

No output

Case 3

Inside

Outside

A

B

P’: output

first

P: output

second

Case 4

Inside

Outside

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A

B

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P’: output

first

A

B

P: output

second

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A

B

P: output

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A

B

P’: output

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A

B

No output

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A

B

No output

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Polygon Clipping in

Homogeneous Coordinates

(Clipping Space Coordinates

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Aout != Bout

C’ color is also linearly interpolated

such as

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C’(r) = A’ (r)+(B’ (r)-A’(r))*t

C’(g) = A’(g)+(B’(g)-A’(g))*t

…………….

Or even for original 3D position (x,y,z) or texture space (u,v) or normal vector (Nx,Ny,Nz)

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Case 4

Case 1

Case 2

Case 4

Return #num of vertex

Ex: left: C0=-C3

C0=A0+t(B0-A0)

C3=A3+t(B3-A3)

A0+t(B0-A0) =

-A3-t(B3-A3)

=>>

(-A3-A0)=t(B0-A0+B3-A3)

A0,A1,A2,A3

B0,B1,B2,B3

Ex: left side

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A

B

P’: output

first

P: output

second

Case 4

Inside

Outside

Ex: left boundary:

C0=-C3

C0=A0+t(B0-A0)

C3=A3+t(B3-A3)

A0+t(B0-A0) =

-A3-t(B3-A3)

=>>

(-A3-A0)=t(B0-A0+B3-A3)

X : A0, B0

Y : A1, B1

Z : A2, B2

W: A3, B3

C

C

Left boundary

C0=-C3

Right boundary

C0=+C3

bottom boundary

C1=-C3

………..

………..

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A

B

P: output

Inside

Outside

Case 1

!Aout = !Bout

Aout!=Bout

Then, Bout is also input into the polygon!

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At most,it will have 6 extra

vertex after clipping with

six planes

Circulate each

Input polygon

Vertex according

To Sutherland-

Hodgman polygon

clipping

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Bounding Volume

  • Simple shape that completely�encloses an object
  • Generally a box or sphere
  • We’ll use spheres:
    • Easiest to work with
    • Though hard to get�tight fits

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Hierarchical bounding volumes

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Recall class about projection example

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