Projective Space

Projective Space:

• Divide through by w

  

• All homogeneous points of the form , are equivalent
• Projects homogeneous points centrally onto the affine plane

Relationship to Perspective:

• In rendering, the w values we generate are proportional to z
  • Equivalence corresponds to perspective projection

More Generally:

Rational splines

• Homogeneous spline curve
  • Spline curve of the form

  

• Rational spline curve
  • Affine projective spline curve