# Rhino Solids and Polysurfaces

## Solid modelling: a simple concept of using primitives as basis for modelling

Solids in Rhino are multiple NURBS surfaces joined into one primitive or een combination of solid primitives. Primitives are basic geometric shapes like a cube, cone, sphere, cylinder and pyramid.

Most operations concerning creating and editing solids can be found in the menu Solid

## Introduction

Example of the use of solids in mechanical engineering

The use of different types of geometry in Rhino was already mentioned in the Introduction to Rhino. For the first exercise we will use Solids to generate a design.

Many industries where accurate 3D models have to be generated use Solids. Solids are widely used in the car, aircraft, mechanical and building industry. A solid is an accurate mathematical description of a volume. This accuracy is crucial for some industries where the tolerances in size are very important. That is one of the reasons why it is used in mechanical engineering.

Rhino has two options of defining a Solid. One is to combine a set of separate surfaces describing a volume into a solid. These surfaces have no thickness and only when combined they define a single, closed volume. These solids are called Poly-surfaces (multiple surfaces). The mathematical description of this geometry is completely different than solid primitives.

The other option is based on the use of a very accurate mathematical defined primitives. Primitives are basic geometric shapes like a cube, cone, sphere, cylinder and pyramid. Several different primitives are available which can be combined into new shapes. The starting point however is always a primitive. This makes it one the one hand easy to use, because the basic building blocks are given, but on the other hand is limits the freedom of designing.

Primitives describe a volume and are called Constructive Solid Geometry or CSG. We will focus on these solids in this part of the explanation because they are easy to make and gives you an idea on the influence of the mathematical description of the geometry, defining the geometry type, on the design process. An influence which you need to understand to make the correct choice in geometry type when you design in the computer.

A few elements which are influenced by the mathematical description are:

• Accuracy of the geometry ( important for manufacturing)
• The shapes it can generate
• The ability to adjust the shape
• The workflow of generating the shapes.

The name of CSG becomes self-explanatory if you look on how the solids can be used to generate geometry. The whole process of generating geometry with CSG is quite straight forward and consists of 3 steps.

1. Generating the primitives
2. Let the primitives interact with each other (Boolean operations) by:
• subtracting one volume from another
• adding one volume to another
• or define the intersection of two volumes into new geometry
3. Editing the resulting volume That means moving corner points, edges or surfaces of the volume.

## Generating Solid Primitives

The first step in designing with CSG is the generation of primitives. Rhino has the option of defining several different primitives. Although the typology of the primitive is predefined, additional settings are available which can be changed. If the object is created it will be placed on the grid unless you used the object snap options to align the primitive to another object. The solids can be created by selecting in the pull down menu Solid. The rollout menu gives access to a range of different primitives. Check the command line for additional options once you activated the command.

### Boolean operations

You can use the primitives as a kind of building blocks similar to a wooden block set used by kids everywhere. In that case you start out with a ground plane and build for example walls and ceilings from cubes and columns from cylinders. Because they can intersect without colliding and there is no gravity in this virtual space they can be moved around freely. This way of generating geometry is quite similar to the form study assignments in previous courses.

However there are additional tools to support the generation of more complex geometry. These options are called Boolean operations.

Union
Shapes that intersect can be combined into a single new object. The command for this is Solid » Union. Check the command line for additional options.
Difference
If you want to make a hole in an object, you can subtract an object the size of the hole from another object (that remains). The command for this is Solid » Difference. Check the command line for additional options.
Intersect
The last option is de definition of the common geometry of two objects. The command for this is Solid » Intersect. Check the command line for additional options.

The command Solid » Boolean Two Objects lets you scroll through the different Boolean operation options which can be useful for exploring the different effects of the different Boolean operations. Although the options of volume interaction ( Boolean operations) and the amount of different primitives are limited the final complexity of the geometry can be quite substantial.

### Editing Solids

Editing Solids

The editing of solids is quite straight forward because there are not that many options for editing a solid. The main options are to move one of the surfaces or edges of the solid or to move the corner points. So three components of the solid can be moved.

#### The corner points

Corner points

You can select the corner point of the solid and then adjust them. However there is a limit on how far you can move them before the geometry starts to distort. This is a limitation of editing a solid.

#### The Edge of the solid

Edge of the solid

Changing the edge of a solid is an effective way of altering the geometry of the solid. It is less prone to distortion like the point edit option.

### The face of the solid

Face of the solid

Also with the movement of the face there is a chance for distortion of the geometry. Especially when it is not moved perpendicular to the face.

So all-in all the options for generating and editing CSG can be quite straight forward.

#### Fillet edges

Fillet solid
Fillet solid1

One option of editing a solid is not discussed yet. This option is called Fillet Edge. This option is widely used in mechanical engineering. It rounds off edges. This is primarily not done for aesthetics but for avoiding extreme stresses at the edges of the object and metal fatigue. However you can use it also as an aesthetic option for smoother edges.

Fillet Edge
Solid » Fillet Edge » Fillet Edge creates round edges
Blend edge
Solid » Fillet Edge » Blend Edge almost similar to Fillet Edge, but has more control points
Chamfer Edge
Solid » Fillet Edge » Chamfer Edge creates cornered edges

#### Cap planar holes

Sometimes when you fillet edges, holes can appear on faces. To close these holes use: Solid » Cap Planar Holes

Cap planar Holes

## Polysurfaces

Besides the option of Constructive Solid Geometry we have in Rhino the Polysurfaces. These are volumes build with NURBS surfaces. Several NURBS surfaces can describe a volume. However the computer doesn't recognize it as a volume, it doesn't know that the surfaces are attached to form a volume. It will see it as a set of loose surfaces. However with the option of "join" you can convert the set of NURBS surfaces to a solid. This can be very useful when adding thickness to a NURBS surface. Normally this has to be done by making an offset of the surface and then closing the sides with a loft. This can be quite tedious work. However it is possible to make an offset of the surface and convert it directly into a solid, hence closing the sides. These options are integrated in the surface editing tools.

### Converting a NURBS to a solid

#### The join option

polysurfaces

The most laborious method of creating a solid from a set of NURBS surfaces is actually building a set of NURBS surfaces which describe a volume and then "join" them. The advantage is of this method is that you can use the tools for NURBS geometry to create extreme complex shapes and then convert them into a solid. If you want to turn the solid back into a set of NURBS to be able to take full advantage of the NURBS editing options you can use the explode icon. This will convert the solid into a set of separate NURBS surfaces.

#### Extrude curve with Solid option on

solid yes

When a curve is extruded into a surface a range of options appear in the command line one of them is the option " solid yes or no" That means that we can extrude a curve directly into a solid volume if we activate the "solid yes option"

#### Offset surface with Solid option on

solid yes

Another command which uses the solid select option is the Surface » Offset surface » solid yes This enables you to create an offset of a Nurbs surface perpendicular to the surface itself. With the solid option on the sides will be automatically closed and the whole object will be converted to a solid.

#### Solid offset planar curve

Curve extrusion into Solid

In the Solid pulldown menu we have two options which convert a NURBS directly into a Solid object. The first one is Solid » Extrude Planar Curve This option allows you to convert an extruded planar curve directly into a Solid similar to the Surface » Extrude curve » solid yes Be aware the curve has to be planar, so completly flat.

#### Solid extrusion surface

Surface extrusion into Solid

The second option is Solid » Extrude surface This option allows you to give thickness to a surface. There is however a catch. The extrude surface option will extrude in one direction. This is different than an offset which is gives an offset perpendicular to the surface.

Surface extrusion vs Surface offset

#### Cap planar holes

Cap planar Holes

When you made an extrusion of a curve and forgot to activate the Solid option on then you could also use the Solid » Cap Planar Holes option. This allows you to cap planar holes.