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Geometric Calculations (3dsmax)

Contents

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Vectors

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Normalization

A normalized vector has a length of exactly 1.0, this value can be multiplied to get exact lengths. ie. A normalized vector multiplied by 5.617 will give you a vector with the length 5.617.

Code: 

normalize vec
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Cross Product

Gives you the vector perpendicular to the two vectors supplied.

Code: 

cross vec1 vec2
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Dot Product

Gives you a relationship between two vectors.

Code: 

dot vec1 vec2

Gives you the cosine of the angle between two normalized vectors.

Code: 

dot (normalize vec1) (normalize vec2)

The result returned by a dot product passed, when acos'd will return the angle in degrees between the two vectors.

Code: 

acos (dot (normalize vec1) (normalize vec2))
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Line

A line can be defined by:

  • 2 points
  • a point of origin and an offset vector
  • a point of origin, a normalized vector and a scalar length
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Mid-Point

The exact center between two points.

Code: 

fn midPoint pt1 pt1 = ((pt1+pt2)/2.0)
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Linear Interpolation (LERP)

Code: 

fn lerp pt1 pt2 alpha = (pt1+((pt2-pt1)*alpha))
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Plane

A plane can be defined by

  • 3 non-colinear points
  • a point and 2 vectors
  • a point and a normalized vector (the normal vector)
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Distance Between a Point and a Plane

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Plane (vector/point)

  • vec = plane vector
  • ppt = a point on the plane
  • pt = point you want to test

Code: 

fn PointToPlaneDist vec ppt pt = 
    (vec.x*pt.x+vec.y*pt.y+vec.z*pt.z) - (vec.x*ppt.x+vec.y*ppt.y+vec.z*ppt.z)
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Acknowledgements

Article inspired by the Geometrical Calculations post on CGTalk

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