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Allowing the blend radius to vary introduces some fundamental differences into the algorithms. The offset-intersection algorithm used to find the spine and spring curves works only for constant-radius blends, because a variable offset is ill-defined on a surface. A figurative rolling ball must be set up at the desired position to evaluate the curves and the blend surface, and a marching algorithm is required to find the approximating curves and surface. Analytic surfaces cannot be used to represent even simple variable radius blends. The spine and spring curves are no longer perpendicular to the plane defined by corresponding points.
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When a variable radius function is specified, there must be some way to indicate exactly where along the blend a particular radius value is obtained.
ACIS uses the geometry of the edge being blended to calibrate this. The parameter of the radius function is the parameter of the edge curve. At a given
v-parameter, a ball of radius
r(v) is set up so that its center is in the plane perpendicular to the edge curve, evaluated at
v.
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Variable Radius Blend Surface Types
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Standard blending supports two mathematical definitions of variable radius blend surfaces. The first is a
rolling ball snapshot blend surface. The second type (introduced in Release 5.0) is a
rolling ball envelope blend surface. Although geometrically similar, sequences of the rolling ball envelope surface are smoother, and their offsets are better behaved. Their spring curves are identical, but the cross sections have a subtly different shape. This allows the rolling ball envelope to be perfectly smooth across transitions between blend surfaces in a smooth sequence of edges.
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The
Advanced Blending Component provides a third mathematical definition of a variable radius blend surface called a
sliding disc. Both the rolling ball snapshot and the sliding disc surface types have a slight crease between faces if the blend rolls across an edge that is smooth but not curvature-continuous and if the radius is varying as it crosses the edge. This can cause near-tangency problems when the surfaces are offset. The rolling ball envelope surface addresses this problem and permits robust performance in operations that use surface offsets.
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The type of variable radius blend surface created (for standard blending only) is controlled by option
bl_envelope_surf. If this option is on (true), a rolling ball envelope blend surface is created. If it is off (false), a rolling ball snapshot blend surface is created. However, applications are discouraged from changing this option setting.
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Simplest Variable Radius Blend Surface Used
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The variable radius blend algorithms construct the simplest blend surface that can represent the geometry requested. For example, if a variable radius blend is specified with a start and an end radius value, and these values are the same, then a constant blend will be made. This behavior is controlled by the option
blend_make_simple, but applications are strongly discouraged from changing this option setting.
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