Mathematics for Computer Graphics Applications Chapter 10

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Mathematics for Computer Graphics
ApplicationsChapter 10

• 2002. 07. 24.
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Algebraic Definition

• Demonstrative or Constructive Definition

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Algebraic Definition

• Algebraic Definition
• Implicit Cartesian equation

Part of a Plane
Perpendicular to x,y plane
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Algebraic Definition

Perpendicular to z axis
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Normal Form

• Normal Distance Direction Cosine

Normal Form
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Normal Form

• Algebraic Normal Form

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Defined by Three Points

• Three noncollinear points

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Defined by Three Points

• Three intersection points

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Vector equation

• Normal distance vector

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Point and Plane

• Implicit form

PT is on the plane
PT PR is on the same side
PT PR is on the opposite side
Point Plane Relationship
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Plane Intersections

• Line segment Plane

Line Plane Intersection
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Plane Intersections

• Two planes

Intersection of two planes