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Visualization: 3D Modelling > Definitions
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Control points (or control
vertices) - These are
points in 3D space that control the shape of the curve or surface they
are attached to. To put it another way, they control how the curve is
"pulled" from a straight line drawn between edit points. The
number of control vertices in each span depends on the degree of the
curve, so if you are constructing a curve from the control points,
several points must be placed to construct the initial segment of the
curve.
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Edit points (also called knots)
- These lie on a curve and mark the connection points between spans.
When constructing a curve with edit points, you need only two points to
create the initial curve segment, regardless of the degree of the
curve.
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Metaballs - These are
objects (e.g., balls, cubes, cylinders, etc.) that have either
attractive or repulsive forces attached to them. When two positive
metaballs come within a certain distance of each other, they attract
and stretch their surfaces towards each other. Negative metaballs do
the opposite, radiating a field of repulsion that either pushes or
erodes away the surface of positive metaballs.
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Mesh - A grid-like
polygonal subdivision of the surface of a geometric model.
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NURBS curve - A type of
spline that can be cut or joined at any point, since each point can be
calculated and located individually. Similarly, NURBS surfaces
can be attached to other NURBS surfaces with different numbers of
spans or isoparms. NURBS is an acronym for Non-Uniform Rational
B-Splines.
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Polygon - In the context
of 3D modelling, a polygon is a multi-sided object composed of edges,
vertices, and faces. An edge
is a line segment that forms one side of a polygon. A vertex
is a point at which two edges meet. A face
is the area enclosed by several edges.
The most basic polygon is a triangular face. Since the three points of
a triangle must always be on the same plane, we can say that all
triangular faces are planar.
Other polygons (e.g. quadrangular polygons, or "quads") may
or may not be planar. Polygon faces can share vertices and edges with
other polygons, or can have unshared edges known as borders
while still being part of the same polygon surface.
A polygon shell is a
group of connected faces with some edges open as border edges. In a polygon
solid, there are no open
borders, and the connected faces form an enclosed volume.
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Span -- The area between
two consecutive edit points.
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Spline - A spline is a
curve in 3D space defined by control points. Splines can be cut or
joined at their edit points. Some common types of splines include
BÉZIER, B-SPLINE, and NURBS.
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Solid - In the context
of 3D modelling, a solid is a 3D object that has an unambiguously
defined inside and outside.
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Surfaces - Like curves,
surfaces are made up of spans, or rather they extend over a given
number of span areas. Whereas a curve is a function of one variable, U,
a surface is a function of two variables, U and V. Most of the methods
for manipulating surfaces are direct extensions of those used for
working on curves. Note that a patch
is a surface segment, an area of the surface covered by one UV span.
The lines separating patches are called isoparms.
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Subdivision surface - A
surface that results from repeatedly refining a polygonal mesh to
create a finer and finer mesh. A subdivision step refines a submesh
into a supermesh by
inserting more vertices. The positions of the vertices of the supermesh
are computed from the positions of the vertices of the submesh, based
on a certain subdivision scheme (note that there are several
subdivision surface algorithms).
Subdivision surfaces can exist on an arbitrary topology, and look
smooth and continuous. They enable the creation of a hierarchy of many
levels of detail, allowing highly detailed modelling in isolated areas
and binding at the base levels.
Questions, comments, and suggestions should be directed to research.support@ualberta.ca.
Revised: August 23, 2006
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