Module 4 NURBS Curves Modeling PDF

MODULE 4 3D MODELING NURBS MODELING NURBS Overview NURBS Overview NURBS (Non-Uniform Rational B-Splines) are one geometry type you can use to create 3D curves and surfaces in Maya. The other geometry types that Maya provides are polygon and subdivision surfaces. Non-Uniform...

MODULE 4 3D MODELING NURBS MODELING NURBS Overview NURBS Overview NURBS (Non-Uniform Rational B-Splines) are one geometry type you can use to create 3D curves and surfaces in Maya. The other geometry types that Maya provides are polygon and subdivision surfaces. Non-Uniform refers to the parameterization of the curve. Non-Uniform curves allow, among other things, the presence of multi-knots, which are needed to represent Bezier curves. Rational refers to the underlying mathematical representation. This property allows NURBS to represent exact conics (such as parabolic curves, circles, and ellipses) in addition to free-form curves. B-splines are piecewise polynomial curves (splines) that have a parametric representation. NURBS Modeling Non-Uniform Rational B-Splines (NURBS) provide a 3D modeling framework based on geometric primitives and drawn curves. You can use NURBS in two ways: Construct 3D models from NURBS primitives. Primitives are simple 3D objects created in the shape of common geometric forms such as cubes, spheres, cones, and so on. Primitives can be a great starting point for many 3D shapes. You can modify the attributes of NURBS primitives to modify their shape. You can also modify NURBS primitives by trimming away portions of their forms, beveling their edges, or by sculpting them into different shapes using sculpting tools. NURBS Modeling Construct NURBS curves that define the basic outline of the 3D form you want to construct, then use the curves as a basis for constructing NURBS surfaces. To find options for constructing and modifying NURBS curves and surfaces: You can draw curves by placing control vertices, or edit points. The curve drawing tools are found in the Create menu. The options for creating and editing NURBS curves and NURBS surfaces are found in the Modeling menu set. You can also find NURBS options on the Curves/Surfaces shelf. Creating NURBS Curves Creating NURBS Curves Draw NURB Curves You can draw a NURBS curve by placing control vertices (CV), placing edit points, or by drawing freehand. If you draw with CVs or edit points, the curve is automatically smoothed; if you draw freehand, the curve exactly follows the path of the tool tip. Before starting to draw, you might want to review or set options for a tool by selecting the option box. For example, select Create > Curve Tools > CV Curve Tool > to see the CV Curve Tool options. Creating NURBS Curves To draw a NURBS curve by placing CVs Select Create > Curve Tools > CV Curve Tool. Click to place the CVs. The first CV looks like a hollow box; subsequent CVs are dots. Hulls are drawn between the CVs as you place them. For each CV after the third one you place, the shape of the curve is drawn. To remove the last CV you placed, press Delete. To switch to editing CVs, press Home or Insert. A manipulator appears on the last CV. Use the manipulator to move the CV, press Delete to delete a segment, or click another CV to edit it. Press Home or Insert again to return to adding CVs. Press Enter to finish the curve. Creating NURBS Curves To draw a NURBS curve by placing edit points Draw with edit points if you want the curve to pass through certain points. This drawing method calculates the positions of CVs based on where you specify edit points. Select Create > Curve Tools > EP Curve Tool. Click to place the edit points. For each edit point after the first one you place, Maya draws the shape of the curve. To switch to editing edit points, press Home or Insert. A manipulator appears on the last point. Use the manipulator to move the point, press Delete to delete a segment, or click another point to edit it. Press Home or Insert again to return to adding points. Press Enter to finish the curve. Creating NURBS Curves To draw a NURBS curve freehand Select Create > Curve Tools > Pencil Curve Tool. Drag to sketch a curve. When you release the mouse button, the curve is drawn. The Pencil Curve tool creates a curve with a large number of data points. Use Curves > Rebuild to simplify the curve. As you draw the curve, points are placed in the view if they are at least five screen pixels from the previous point. If you sketch in an orthographic view (front, top, or side), the curve is placed on the view plane at the origin. If you sketch in the perspective view, the curve is placed on the grid plane. Degree of NURBS curves and surfaces Degree of NURBS curves and surfaces Maya has the ability to create curves with a degree of 1, 2, 3, 5, or 7. The default degree in Maya is 3, which has four CVs for the first curve span. A curve degree of 3 is sufficient for almost any modeling task. You may want to use degree 5 or 7 curves if you are producing 3D surfaces for subsequent export to a CAD application for industrial design purposes. Degree of NURBS curves and surfaces Degree is a mathematical property of a curve or of a surface that controls how many CVs (control vertices) per span are available for modeling. The degree is always represented mathematically as a positive whole number. Degree can be thought of as the curve or surface’s degree of freedom to bend. A degree 1 curve connects its edit points with straight lines in a polygonal fashion. A degree 2 curve can have one bend between edit points, and so on. Degree of NURBS curves and surfaces Degree is a mathematical property of a curve or of a surface that controls how many CVs (control vertices) per span are available for modeling. Degree of NURBS curves and surfaces Degree can be thought of as the curve or surface’s degree of freedom to bend. A degree 1 curve connects its edit points with straight lines in a polygonal fashion. A degree 2 curve can have one bend between edit points, and so on. Curvature and Continuity Curvature and Continuity Curvature Curvature is a measure of the rate of directional change over a distance. Curvature and Continuity Curvature Curvature is measured by fitting a circle into the curve, then taking the reciprocal of the circle’s radius. In this figure, at point x the curve is best described by a circle with radius r. At this point, the curvature is 1/r. We use the reciprocal, 1/r, instead of just r because a flat line has an infinite radius. Taking the reciprocal gives us a curvature of 0 instead of infinity. Curvature and Continuity Curvature Curvature and Continuity Continuity for NURBS curves and surfaces Continuity is a measure of how smoothly two curves or surfaces flow into each other at their meeting point. The type of curvature in a set of curves and surfaces may be important if you need to subsequently export your Maya NURBS surfaces to a CAD software application. Curvature and Continuity Continuity for NURBS curves and surfaces Positional (G0) The endpoints of the two curves or surfaces meet exactly. Note that the two curves or surfaces can meet at any angle and still have positional continuity. Curvature and Continuity Continuity for NURBS curves and surfaces Positional (G0) Curvature and Continuity Continuity for NURBS curves and surfaces Tangent (G1) Curves or surfaces that have tangent continuity also have positional continuity, plus the end tangents match at the common endpoint. The two curves will appear to be travelling in the same direction at the join, but they may still have very different apparent “speeds” or curvature. Curvature and Continuity Continuity for NURBS curves and surfaces Tangent (G1) For example, in this figure, the two curves have the same tangent (the double-arrow line) at the join (the dot). But the curve to the left of the join has a slow (low) curvature at the join, while the curve to the right of the join has a fast (high) curvature at the join. Curvature and Continuity Continuity for NURBS curves and surfaces Curvature (G2) Curves or surfaces that are curvature continuous have tangent continuity, plus the curvature of the two curves matches at the common endpoint. The two curves appear to have the same speed at the join. Bezier curves Bezier Curve Bezier curves are a subset of NURBS curves that are composed of two types of control vertices, anchors and tangents. Anchors lie on the curve and determine the origin of tangents. Tangents determine the shape of the curve leading to an adjacent anchor. Bezier Curve Bezier Curve Since Bezier curves are a subset of NURBS curves, you can perform the majority of NURBS operations to Bezier curves as well. You can also perform NURBS operations on combinations of Bezier curves and NURBS curves. In general, an operation involving all Bezier curves results in a Bezier curve while operations involving a combination of Bezier and NURBS curves results in a NURBS curve. Use and Limitations of NURBS Use and Limitations of NURBS Early in the history of 3D computer graphics, NURBS were used to create organic surfaces and even characters. However, as computers have become more powerful and the software has developed more advanced tools, most character modeling is accomplished using polygons and subdivision surfaces. NURBS are more ideally suited to hard-surface modeling; objects such as vehicles, equipment, and commercial product designs benefit from the types of smooth surfacing produced by NURBS models. Use and Limitations of NURBS All NURBS objects are automatically converted to triangles at render time by the software. You can determine how the surfaces will be tessellated (converted into triangles) before rendering, and you can change these settings at any time to optimize rendering. This gives NURBS the advantage that their resolution can be changed when rendering. Models that appear close to the camera can have higher tessellation settings than those farther away from the camera. Use and Limitations of NURBS One of the downsides of NURBS is that the surfaces themselves are made of four-sided patches. You cannot create a three- or five-sided NURBS patch, which can sometimes limit the kinds of shapes that you can make with NURBS. If you create a NURBS sphere and use the Move tool to pull apart the control vertices at the top of the sphere, you'll see that even the patches of the sphere that appear as triangles are actually four-sided panels. Use and Limitations of NURBS Here you can see that pulling apart the control vertices at the top of a NURBS sphere reveals that one side of each patch has been collapsed. END OF MODULE