## Kinds of paths

The terminology for paths that exist in 3d space is more fragmented than for polygonal objects. Some programs will call them "splines" (Cinema 4D), some "shapes" (Max) and others "curves" (Maya). But the basic usage remains the same. Paths are straight or curved line segments that have no mass themselves (and so typically will not appear in a rendered image), but can be used as a foundation for a more complex object.

While paths can typically be easily converted from one kind into another you are usually given the option of starting with a particular type, linear, bezier, quadratic, and others depending on your program. Just keep in mind that they are all the same type of object and can be edited in the same ways.

Also remember that all paths can have multiple points along the paths, and can be connected from start to end to form loops, but they can not "branch out" into forked shapes.

### Straight lines (Linear)

Straight line segments of course are paths that move directly between two points. We can string them together to form lines that approximate a curve if we like, but the individual segments will always be made up of control points.

### The bezier curve

Bezier curves add a new option to path editing; the control point "handle".

Since bezier lines are probably more often used by Graphic Design students than 3d modeling and animation students, I've written out most of how bezier and b-plines in that section, which can be found at the following link...

writings_tutorials_design_basics.html

Of course like any line they exist in a 3d space. Keep in mind that the *handles* can also be on different planes than the main vertices as well.

Other forms of lines allow you to have "handles" that are tied to two segments of a path at once.

## Path Modifiers

As said, regardless of what type of path you are using the rules will mostly be the same. There are 3 ways in which you'll be modifying the path.

1. Editing the control points.
3. Changing the interpolation of the path.

Editing the control points of a path is fairly similar to editing the vertices of a polygonal object. Grab a vertex, move it with the move tool. Similarly some programs let you select the entire line segment as you would an edge within a mesh or the entire path. Click and drag a path point to move it around (Rememember that you can select more than one point at a time).

The real use of paths becomes clear when you apply modifiers.

### Extrude

An extrude effect added to a spline creates a simple wall of geometry. It can be thought of as the 2d version of a extrude operation performed on a polygon face.

### Lathe

The images to the right depict a path that has been drawn to resemble one side of a wine glass. It's hard to see without being able to rotate around, but all of the points in the path are on the same plane, and are .

When we apply a simple "lathe" modifier to this path we end up with a full

Like many path modifiers the "lathe" modifier is based on an adjustable axis. In this case the axis dictates the point of rotation. Since the axis is in a similar place to the path axis (shown in the top image) the path is swept around that point to form the shape.

Here is something important to remember. At this point if we wanted to increase or decrease the number of rotational polygon segments that are being produced we would be able to do that in the *lathe* modifier settings, and *not* the original path settings. If we want to change the number of vertical polygons then we would change the original path settings (see the section on interpolation below).

Most lathe modifiers will default to a 360 degree turn but will allow you to do partial turns as well.

### Sweep

Now lets look at the images below to see the effect of a "Sweep" modifier. This modifier will use two paths. One path will be the actual shape of the new object, thee other path will dictate the path that shape will move along.

### Loft

A "loft" modifier for splines can mean different things in different programs, and work in even more varied ways. Generally it will describe a way to transition between two or more spline shapes.

This can be useful for object that transition from one shape to another. Such as a round electrical cord becoming the square plug end. Or perhaps for a blanket you want to have wrinkles and folds without using physics.

Now what did we mean earlier when we talked about changing the interpolation of the path?

## Path interpolation

The first important concept to remember is that all path objects that have *any* curving to them will be making use of intermediate points.

Most programs have at least 3 basic forms of interpolation.

• None.
• Linear.

To the right you can see wireframe views of 3 objects made by applying a sweep modifier to a simple bezier curve (the second spline is a simple box). Notice the difference between the three forms of intermediate point generation and how they change the polygon count.

Obviously if you were to set the interpolation to "none" there wouldn't be a point to even using a bezier curve in this instance. It can be useful if you want to preview different possibilities or if your program has detail settings that allow you to lower the details in complex scenes for faster previewing in the editor window.

"Uniform" gives us a smooth curve, but notice the number of cuts in the center of the shape, where the line is fairly straight. In this middle area the polgyons being made by the uniform interpolation are being wasted. This can be useful if the shape is going to be further deformed, during animation for instance, but if not then there is not point to having these extra polys.

"Adaptive" is usually the default, and best, value for this property. It allows the curve to be seen, but does not place extra cuts where they are not needed, giving the most effecient mesh.

Typically the "uniform" setting will also allow you to change the number of cuts. Entering "10" usually means there will be 10 segments. The adaptive setting might have a more confusing input. It might have an extra option that comes in degrees. If so, then just keep in mind that the setting is changing when a new cut is added based on a threshold, measured in rotation. So if the bezier curve alters is direction more than the given thresheld, from the previous cut, then a new cut is added.

## Common uses

There isn't just one particular use where you will suddenly say "I need paths" for this. The best question you might ask at some point during initial creation of an object is "is there a constant direction or consistent shape to the surface that might be defined by a path?"

We used the age-old wineglass and wiring already so let's just list some different objects to try and illustrate the diversity of objects that can be made with paths.

### Architectural curving

If your software has a path deformer of some kind then you can use paths to guide the direction of more complex objects. Take a curved stairwell for instance. A simple helix-shaped path

### Wall baseboard / molding / dados

You've probably seen protective boards at the bottom of walls that help ensure furniture and feral children are not placed directly against a wall surface, or decorative molding that runs along the top of the wall. Both of these are good candidates for sweep modifiers.

### Decorative details & Miscellaneous ideas

Here a few other examples of how 3D paths can be used.

>
UC
>

## Using spline modifier origin

In many programs modifiers like symmetry objects or certain deformers will have different effects on an object depending on the position of their own axis. For spline modifiers this is very evident in the Lathe modifier.

The geometry created by a lathe function will always "spin" around the axis of the modifier and NOT the spline that it is affecting. This is extremely important to remember.