Nurbs surface patch

It has many strengths due to the flexibility. Additionally, a number of 3D scan data processing software manufacturers have created simple and automated workflows to create the NURBS surface model from a 3D scan of an object. This quick and efficient way to generate a 3D model is outlined below to show how simple the process can be.

Parametric 3D Modeling — This form of 3D modeling is based on 2D and 3D sketches which define an objects geometry mathematically. Incorporating techniques like lofts, sweeps and revolves to these sketches creates features that can be trimmed, extruded, offset, shelled, drafted, etc. Parametric 3D CAD modeling is a history-based approach where all entities created can be accessed and edited. When the proper relationships and constraints are applied, editing a parametric model can be made very efficient as designers can make changes at pre-defined parameters.

This type of 3D modeling is widely used when an object has prismatic shapes, but it can also be used for and objects with complex curvature. When geometry is tough to match with mathematically defined features, NURBS modeling is a great technique to explore.

When this technique is used on a raw scan data mesh, it provides you with great accuracy. A NURBS model does not have the same ability to modify as a parametric model, but it will provide a more accurate representation of the measurements from the 3D scan geometry. Imagine using 3D scan data of a human limb to create custom prosthetics.

NURBS modeling provides the most simple and efficient workflow, while maintaining the highest accuracy to the 3D scan data. Parametric modeling of the limb geometry would be almost impossible to achieve similar accuracies to NURBS modeling.

Hybrid Modeling — when you have an object that includes a variety of prismatic and freeform shapes, a hybrid model may be the best approach.

Feature based modeling can be used where a design-intent geometry is required for the design process, and the NURBS surfaces can be used to include the highest complexity curvature or freeform shapes. Below is a great example where the front end of an ATV was modeled using both prismatic and NURBS techniques resulting in a deliverable that allowed for aftermarket part design without the manual effort of parametrically modeling all features. Solutions Industries Applications. Necessary cookies are absolutely essential for the website to function properly.

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For example, quadruple the control points for a fourth-order curve if you wish to make the curve pass through that point. Another technique is to construct a knot vector that generates positional continuity of the endpoints of the curve. When error checking is activated, the software sends error messages and does not display the NURBS surfaces associate with the faulty trim data. Likewise, the end points of piecewise linear curves and the NURBS curves used to form a compound trimming curve must touch.

The trim region is the area of the NURBS surface in which the surface domain is trimmed by a closed directed loop composed of one or more trimming curves in s-t space, where the interior of the loop is defined to be the region to the left of the loop.

The surface domain can be trimmed by many such loops, as long as they describe a consistent region. The loops can neither touch nor intersect except at their end points, which must touch , and their orientations must also be consistent. The following figure illustrates a set of 5 loops that describe a valid trimming region. If no trimming information is provided, the entire surface is drawn.

If any trimming loops are given, the outer loop or loops must be counterclockwise. Thus to describe a region that consists of the whole surface minus a small circle in the middle, two trimming loops must be specified: one running clockwise around the circle, and another running counterclockwise around the entire s-t domain.

A trimming loop can be described either as piecewise linear curves a series of s-t coordinates locating successive points along a path , or as NURBS curves in the s-t plane. A loop can be described either by a single NURBS curve, by a piecewise linear curve, or as a series of curves of either type joined head to tail.

Each trimming loop is surrounded by a bgntrim and endtrim subroutine pair. A single curve defines the first two trimming loops; the third loop consists of three segments, connected head to tail. The last point of each curve segment must touch the first point of the next, and the last point of the last segment must touch the first point of the first segment. The nurbssurface subroutine describes the untrimmed surface and appears before any trimming information. The trimmed surface description is bracketed by a bgnsurface and an endsurface subroutine pair.

The other subroutines specifically related to the properties of NURBS surfaces are setnurbsproperty and getnurbsproperty. These subroutines allow the user to set and get drawing tolerances of various types. All the subroutines in the example , except for the getnurbsproperty subroutine, can be used in display lists. In this implementation, NURBS surfaces described in display lists usually run faster because some of the display computations can be cached between display list traversals.

All the parameters are passed with strict call-by-value semantics. This means that the system copies all values, including trim points and control points, at the time of the call. For example, if you have an array containing control points, and you define a NURBS surface in a display list using it and then change the value in your array, the display list will continue to draw the surface using the original control point values. The structure of the parameters is analogous to those for the nurbssurface subroutine, except, of course, there is only one dimension to describe.

If a single curve defines the entire trimming loop, both ends of the curve must lie at the same point and must be included in the parameter count. To define a piecewise linear trimming curve, use the pwlcurve subroutine. The syntax is as follows:. It is as important to increment the trim point count as it is to duplicate the last point. In other words, although the last and first points are identical, they must be specified and counted twice.

The setnurbsproperty subroutine changes various properties that control the rendering of NURBS curves and surfaces. The call uses this format:. Each has some reasonable default value but can be changed to affect the accuracy of some part of the rendering. You can get the current value of any of these properties with a call to the getnurbsproperty subroutine.