Curves in 3D Studio Max

Meshes: Polygons

Triangles are most common. Smoothing is done by averaging shading values of adjacent polygons. Advantage is that they are simple and flexible to use. Disadvantage is that it can take many more polygons to represent a smooth surface than it would with spline objects.

Primitives

Max probably uses instructions for creating objects such as spheres and cubes. As a result they are very efficient to store. However, limited amount of manipulation is possible. Can convert primitives to editable meshes.

Representation

Curves can be represented as

• explicit functions (y = f(x)) - good for generating points but dependent on choice of axes and can be ambiguos if function multivalued (i.e. not one-to-one).
• implicit functions (f(x,y)=0) - good for testing to see if a point is on a curve is not good for generating a sequence of points on a curve.
• parametarized functions (x=f_x(t), y=f_y(t), 0<=t<=1) - good for generating a sequence of points along a curve and works if function is multivalued.

Interpolation vs Approximation

• Interpolating spline: curve goes directly through the control points
• Approximating spline: curve does not go directly through the control points. The points lie near the curve and their position controls the shape of the curve. Allows a wider margin of error in the placement of the control points and tends to create a smoother curve.

Splines

Polygons always have straight edges whereas splines are curved. Of course, at render time, the splines are converted to polygons but the resolution level of the polygons can be chosen at render time. For example, you can work with a low level of detail making it easy to render in the viewport and then choose a high level of detail at render time. With polygons, you can have only one level of detail.

There are two basic types:

• Bezier curves
  • Bezier curves are approximating splines named after the man who invented it. It is defined by 4 control points, however, longer curves are obtained by connecting together multiple bezier curves together.
• NURBS (non-uniform rational B-spline).
  • Like an interpolating spline it goes through the first and last control points, however, like an approximating spline id does not go through the intermediate control points. In addition, there is a set of "edit points" also called "knots" that lie exactly on the curve. Thus Nurbs can be adjusted using the control points if you want smoothness or the knots if you want precision. This gives you the advantages of both interpolating and approximating splines.
  • The B in B-spline is short for basis. B -splines are approximating splines.
  • Advantage is that subdivision can be done on the fly based on how close the object is to the camera etc.
  • Disadvantage: Demanding on processor at render time.

To render spline objects, the splines are converted to polygon meshes. However, since the splines themselves are curved, one can increase the smoothness by increasing the resolution of the spline-to-polygon conversion.

Subdivisional surfaces: combine the advantages (simplicity and flexibility) of polygonal objects with the advantages of patches (smoothness). Recursively subdivide polygons as necessary.

[top]

[Home]