Rhino Curves and points
Creating Curves
Introduction
Certain properties of NURBS geometry make the NURBS perfectly suitable for designing complex geometries like double curves surfaces. The form freedom which NURBS supports and the possibilities to adjust them give the designer a wide range of 3 dimensional forms to explore. To be able to make the right decision a designer will need a basic understanding of the topology of the geometry which will be used in the design process. NURBS geometry are widely used in computer aided design CAD, computer aided manufacturing CAM and computer aided engineering CAE software. It supports industry standards like IGES, STEP and ACIS. The ability to intuitively and predictable adjust the curves and surfaces make it an power full geometry suitable for design.The NURBS are a generalized derivative of the Bezier curve. ( Pierre Bezier worked as engineer for Renault , development started in the 1960’s to find a method to represent curved lines and surfaces for car design).
Bend lines created in Maya and Rhino are called CURVES, that are based on Bezier Curves and are used as the basis for NURBS and Polygon modeling within Maya or only as basis for NURBS modelling in Rhino. The way the curves are defined makes is possible to draw straight lines and smooth curves. The concept of the structure of the lines where inspired on techniques used in the shipbuilding industry at the beginning of the 19th century. The wooden planks of the ships hull where bend by adding weights at different points on the plank. The amount of bend of shape of the bend could be adjusted by increasing the weight or the position of the weights.
The concept of deformation was digitally implemented in to the curves definition. With the effect that the curve in not only defined by the start and end point of the line but also by the weights between the two. These position and strength of the weights will determine the amount of bending of the curve. The amount of weights between the start and end point are defined by the Degree . Degree 1 will mean that there are only the start and the end point. This will generate a straight line. Degree 3 will contain next to the start and end points two weights to define the curve. By increasing the degree more weights are added and the possibility to deform the line will increase.
Parts of the geometries topology is comparable with the Bezier curve. The surface supports the same use of weighted vertices to define the curvature and shape of the geometry. The geometry itself can be seen as a combination of two sets of "parallel" curves placed at a crosswise angle, with the mesh defined between the curves. Resulting effect is that the surface can support two different degrees, one in each direction. These curves on the surface are called ISOPARMS. The ISOPARM will behave almost the same as a Bezier curve. Selecting and moving a vertex on a surface will basically deform the ISOPARM causing the surface to deform. The more ISOPARMS on a surface, the more vertices are generated to deform the surface OR the higher the degree of the curves, the more vertices will be generated per ISOPARM and surface as a whole.
The NURBS surface contains several different components. We have already found out that the NURBS surface contains ISOPARMS. The ISOPARMS are the sets of crosswise angled curves on the surface. They are in fact the curves where the surface is based on, but are part of the surface itself.
Getting started
Rhino is primarily a model program. That means that it is developed for generating geometry. The result of this focus is that the interface of Rhino is quite straight forward. We have seen, in the introduction, that there are three methods of accessing the commands in Rhino. There are the pulldown menu's , the command line and the toolbox.
When you want to generate 3d NURBS geometry you often start with the definition of a set of curves and from those curves you can generate the 3d geometry. Because Rhino only has a limited support of history, any changes in the curves will not always translate to the geometry made by those curves. A plugin called Grasshopper was developed to explicitly make these parametric connections.
2D objects
The options of drawing 2D objects are extensive.
In Rhino it is possible to draw various types op 2D objects:
- Points
- Line
- Lines
- Polyline
- Curves
Creating Points
Points can be very useful to point out locations in your model or act as reference point for other types of geometry. A point itself has no dimensions, only a location. Therefore it will not be visible in the render/shaded mode.
Points can be created one-by-one or in grids/clouds.
Creating Lines
There a two different line types used in Rhino:
- Line
- Polyline
The main difference is that a line is always straight, a polyline can contain curved parts.
Lines can be used as construction lines for other geometry or as input for surfaces. There are a few ways to draw a line. (from left to right in the menu)
- Line Single line
- Polyline Draw a line out of segments, the segment remain attached
- Segmented Line Draw a line out of segments, the segment remain separate
- From Midpoint
- Surface Normal
- Verical to CPlane draw a line vertical to the construction plane
- Line by four points draw a line from four points
- Bisector draw a line that bisects two lines
- Angled draw a line at a specified angle from another line
- Perpendicular from curve
- Perpendicular from 2 curves
- Tangent from curve
- Tangent from 2 curves
Creating Curves
Rhino represents all curves: lines, arcs, circles, and free-form curves (in fact everything you can create from the Curve menu) as NURBS curves. Whenever Rhino asks you to select a curve, you can select any of these curve objects. You can create curves from scratch: lines, arcs, circles, ellipses, free-form curves, and many others. You can also create curves from existing objects: blend between two curves, cut sections and contour curves through existing surfaces, and project curves onto surfaces.
circle and ellips
arcs
curves
Editing Curves
Rhino supports an extensive array of tools to edit curves. Like all the other tools they can be accessed by the pulldown menu or by the tool box. The commands can also be accessed by typing them in the command line. The curves can be edited in several ways. Unlike Maya the editing options on a component level are limited to point editing. There are three main editing options.
- Edit the composition of the curve. In this case the curve shape is not changed but the way it is constructed is changed
- The second option is the editing of the control points of the curve
- The third option is the change of the shape of the curve.
Attaching curves
Curve Edit Tools – Match
The match tool is used to align the curves to ensure a straight or smooth connection. Because Nurbs objects often consist of multiple surfaces the alignment of the surfaces becomes crucial. Complex smooth surfaces like used in free Form architectural design often consist of multiple double curved surface which are aligned to generate a uniformly smoothed multipatch surface.
There are three align options.
- C0 – Hard connect - position
- C1 – Smooth connect by continuation of the tangency of the curve. The tangency is the curvature at the end of the curve. Tangency
- C2 – Smooth connect by continuation of the curvature of the curve. This smoothes the curves in a single fluent form. Curvature
- Edit - Join. Joins attached lines and curves into a single line
Detaching curves
- Edit – Trim. Curves can be detached by using a cutting line similar how the tool is used in Acad. With trim a part will be deleted.
- Edit – Split. Curves can be detached similar to the Trim tool with the difference that no curves will be deleted. In Rhino there is the option of defining a point on a curve and use it as a cutting point this makes it possible to cut the curve at any point. To select the point option use the command line.
Changing the composition of the Curve
Changing the composition can be useful when geometry is generated from a curve. A curve can be completely rebuild changing the degree or the amount of control points. The control point is the weighted points on the curve. An Edit point is a point on the curve itself. The edit point makes it much easier to edit because they are directly fixed on the curve itself. The other option is to insert new edit points. In rhino there is also an option which makes it possible to divide the curve in precise the same length pieces.
- Making the edit points visible- use the icon on the toolbar or press F10 – to hide the edit points press F11
- Edit – Rebuild – Changes the amount of control points and or the degree.
- Edit - Control Points – Series of commands for control point and edit point editing .
- To add Control Points use the Insert Knot option – This will insert a Control Point without rearranging the existing ones.
- The Insert Edit point - The other edit points and control points are moved to accommodate the new edit point.
Altering the shape of the curve
- Extend Curve. Extents the curve
- Fillet Curves. Smooths the edges of the curve
- Chamfer Curves. Slices the corners of the curves
- Offset Curve. Makes a copy of the curve with an offset
- Cross section profiles. Makes it possible to generate from a set of profiles a set of section lines.
Creating 3D objects
Curve based geometry
Curve based geometry is based, as the names already makes clear, on curves.
See Curve Based Modeling for detailed information.
Primitives
Rhino has also the option of creating 3D primitives. However these primitives are not NURBS but they are called Solids. The solid is in Rhino a NURBS based geometry where the topology of the surfaces are known. This makes it possible to see these solids as solid geometries and not as separate surfaces. Similar to Maya there are only a limited amount of options available to generate 3D geometry based on 2D curves.
See Solid Modeling for more information.
