3D Game DesignChapter 4. Hierarchical Scene Representation( 4.3 Rendering a Scene Graph )

Networked Virtual Computing Lab.Yun-Seok Lee

Basic Concept

View frustum The portion of the world to be viewed

The world bounding volume is used to determine whether the object is culled or not.Geometry classes could provide a Boolean flag indicating whether the world data is current or not.

1. Culling by Spheres

View frustum plane is specified by N • X = d

The culling condition N • C – d < -r N : unit-length vector that points to the interior of the

frustum C : center of the bounding sphere r : radius of the sphere The left side of the inequality is the signed distance f

rom C to plane.

2. Culling by Oriented Boxes

A box is culled. If all its vertices are outside the

plane.

Vertices, distance and

The culling condition The test is identical to that of sphere, except that r

is known for the sphere but must be calculated for each test of a box.

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radius

3. Culling by CapsulesA capsule A radius r > 0 A parameterized line segment. P + tD, where D≠0 and t∈[0,

1].The signed distances from plane to end points.

The culling condition if

if // culled else if

if // culled

dPN

0

dDPN )(1

0 DN

rdPN

0 DN

rdDPN )(

4. Culling by LozengesA lozenge A radius r > 0 A parameterized rectangle P + sE0 + tE1, where E0 ≠ 0, E1≠0,

E0 E• 1=0, (s,t)∈[0,1]2.The four rectangle corners P00 = P, P10 = P + E0, P01 = P + E1, P11

= P + E0 + E1.The signed distances If any of the signed distances are nonnegative, then the lozenge is

not culled. The distance of the nearest corner to the plane is nonnegative, th

en the lozenge is not culled.

dPN ijij

5. Culling by CylindersA cylinder A radius r > 0. a height h∈[0,∞]. A parameterized segment C + tW, where |W|=1 and t∈[-h/2, h/2]. U, V and W is an orthonormal set. , and

The culling condition if

if // culled else if

If or If / culled

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)(1

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6. Culling by EllipsoidsAn ellipsoids , where, M is a positive definite m

atrix. If C + sN is outside the frustum plane, an ellipsoid is out

side.A radius of an ellipsoid The points X that project to the end points of the interval

must occur where the normals to the ellipsoid are parallel to N.

-> -> -> -> // culled

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