Polygon Vertices

A polygon is a surface constructed using three or more points known as vertices. The surface between these vertices is a face. A mesh is a series of faces that share two or more vertices. The most common way to create a polygon surface is to start with a primitive (such as a plane, sphere, or cube) and then use the numerous editing tools to shape the primitive gradually into the object that you want to create.

When all of the vertices of a polygon are along a single plane, the surface is referred to as planar. When the vertices are moved to create a fold in the surface, the surface is referred to as nonplanar (see Figure 3.1). It’s usually best to keep your polygon surfaces as planar as possible. This strategy helps you to avoid possible rendering problems, especially if the model is to be used in a video game. As you’ll see in this chapter, you can use a number of tools to cut and slice the polygon to reduce nonplanar surfaces.

Polygon Edges

The line between two polygon vertices is an edge. You can select one or more edges and use the Move, Rotate, and Scale tools to edit a polygon surface. Edges can also be flipped, deleted, or extruded. Having this much flexibility can lead to problematic geometry. For instance, you can extrude a single edge so that three polygons share the same edge (see Figure 3.2).

This configuration is known as a nonmanifold surface, and it’s a situation to avoid. Some polygon-editing tools in Maya do not work well with nonmanifold surfaces, and they can lead to rendering and animation problems. Another example of a nonmanifold surface is a situation where two polygons share a single vertex but not a complete edge, creating a bow-tie shape (see Figure 3.3).

Polygon Faces

The actual surface of a polygon is known as a face. Faces are what appear in the final render of a model or animation. There are numerous tools for editing and shaping faces, which are explored throughout this chapter and the next one.

Take a look at Figure 3.4. You’ll see a green line poking out of the center of each polygon face. This line indicates the direction of the face normal; essentially, it’s where the face is pointing.

The direction of the face normal affects how the surface is rendered; how effects such as dynamics, hair, and fur are calculated; and other polygon functions. Many times, if you are experiencing strange behavior when working with a polygon model, it’s because there is a problem with the normals (see Figure 3.5). You can usually fix this issue by softening or reversing the normals.

Two adjacent polygons with their normals pointing in opposite directions is a third type of nonmanifold surface. Try to avoid this configuration.

Working with Smooth Polygons

There are two ways to smooth a polygon surface: you can use the Smooth operation (from the Modeling menu set, choose Mesh ➣ Smooth), or you can use the Smooth Mesh Preview command (select a polygon object, and press the 3 key).

When you select a polygon object and use the Smooth operation in the Mesh menu, the geometry is subdivided. Each level of subdivision quadruples the number of polygon faces in the geometry and rounds the edges of the geometry. This also increases the number of polygon vertices available for manipulation when shaping the geometry (see Figure 3.6).

When you use the smooth mesh preview, the polygon object is actually converted to a subdivision surface, or subD. Maya uses the OpenSubdiv Catmull-Clark method for subdividing the surface. You can read more about subdivision surfaces later in this chapter in the section “Using Subdivision Surfaces.”

When a polygon surface is in smooth mesh preview mode, the number of vertices available for manipulation remains the same as in the original unsmoothed geometry; this simplifies the modeling process.

• To create a smooth mesh preview, select the polygon geometry and press the 3 key.
• To return to the original polygon mesh, press the 1 key.
• To see a wireframe of the original mesh overlaid on the smooth mesh preview (see Figure 3.7), press the 2 key.

The terms smooth mesh preview and smooth mesh polygons are interchangeable; both are used in this book and in the Maya interface.

When you render polygon geometry as a smooth mesh preview using mental ray^®, the geometry appears smoothed in the render without the need to convert the smooth mesh to standard polygons or change it in any way. This makes modeling and rendering smooth and organic geometry with polygons much easier.

Understanding Curves

All NURBS surfaces are created based on a network of NURBS curves. Even the basic primitives, such as the sphere, are made up of circular curves with a surface stretched across them. The curves themselves can be created several ways. A curve is a line defined by points. The points along the curve are referred to as curve points. Movement along the curve in either direction is defined by its U-coordinates. When you right-click a curve, you can choose to select a curve point. The curve point can be moved along the U-direction of the curve, and the position of the point is defined by its U-parameter.

Curves also have edit points that define the number of spans along a curve. A span is the section of the curve between two edit points. Changing the position of the edit points changes the shape of the curve; however, this can lead to unpredictable results. It is a much better idea to use a curve’s control vertices to edit the curve’s shape.

Control vertices (CVs) are handles used to edit the curve’s shapes. Most of the time, you’ll want to use the control vertices to manipulate the curve. When you create a curve and display its CVs, you’ll see them represented as small dots. A small box indicates the first CV on a curve; the letter U indicates the second CV.

Hulls are straight lines that connect the CVs; they act as a visual guide. Figure 3.9 displays the various components.

The number of CVs per span minus one determines the degree of a curve. In other words, a three-degree (or cubic) curve has four CVs per span. A one-degree (or linear) curve has two CVs per span (see Figure 3.10). Linear curves have sharp corners where the curve changes directions; curves with two or more degrees are smooth and rounded where the curve changes direction. Most of the time, you’ll use either linear (one-degree) or cubic (three-degree) curves.

You can add or remove a curve’s CVs and edit points, and you can also use curve points to define a location where a curve is split into two curves or joined to another curve.

The parameterization of a curve refers to the way in which the points along the curve are numbered. There are two types of parameterization:

Uniform Parameterization  A curve with uniform parameterization has its points evenly spaced along the curve. The parameter of the last edit point along the curve is equal to the number of spans in the curve. You also have the option of specifying the parameterization range between 0 and 1. This method is available to make Maya more compatible with other NURBS modeling programs.

Chord Length Parameterization  Chord length parameterization is a proportional numbering system that causes the length between edit points to be irregular. The type of parameterization you use depends on what you are trying to model. Curves can be rebuilt at any time to change their parameterization; however, this will sometimes change the shape of the curve.

You can rebuild a curve to change its parameterization (using the Modeling menu set under Curves ➣ Rebuild). It’s often a good idea to do this after splitting a curve or joining two curves together, or when matching the parameterization of one curve to another. By rebuilding the curve, you ensure that the resulting parameterization (Min and Max Value attributes in the curve’s Attribute Editor) is based on whole-number values, which leads to more predictable results when the curve is used as a basis for a surface. When rebuilding a curve, you have the option of changing the degree of the curve so that a linear curve can be converted to a cubic curve and vice versa.

Understanding NURBS Surfaces

NURBS surfaces follow many of the same rules as NURBS curves since a network of curves defines them. A primitive, such as a sphere or a cylinder, is simply a NURBS surface lofted across circular curves. You can edit a NURBS surface by moving the position of the surface’s CVs (see Figure 3.11). You can also select the hulls of a surface, which are groups of CVs that follow one of the curves that define a surface (see Figure 3.12).

NURBS curves use the U-coordinates to specify the location of a point along the length of the curve. NURBS surfaces add the V-coordinate to specify the location of a point on the surface. Thus a given point on a NURBS surface has a U-coordinate and a V-coordinate. The U-coordinates of a surface are always perpendicular to the V-coordinates of a surface. The UV coordinate grid on a NURBS surface is just like the lines of longitude and latitude drawn on a globe.

Just like NURBS curves, surfaces have a degree setting. Linear surfaces have sharp corners (see Figure 3.13), and cubic surfaces (or any surface with a degree higher than 1) are rounded and smooth. Often a modeler will begin a model as a linear NURBS surface and then rebuild it as a cubic surface later (Surfaces ➣ Rebuild ➣ ❒).

You can start a NURBS model using a primitive, such as a sphere, cone, torus, or cylinder, or you can build a network of curves and loft surfaces between the curves or any combination of the two. When you select a NURBS surface, the wireframe display shows the curves that define the surface. These curves are referred to as isoparms, which is short for “isoparametric curve.”

A single NURBS model may be made up of numerous NURBS patches that have been stitched together. This technique was used for years to create CG characters, but now most artists favor polygons or subdivision surfaces. When you stitch two patches together, the tangency must be consistent between the two surfaces to avoid visible seams. It’s a process that often takes some practice to master (see Figure 3.14).

Surface Seams

Many NURBS primitives have a seam where the end of the surface meets the beginning. Imagine a piece of paper rolled into a cylinder. At the point where one end of the paper meets the other end, there is a seam. The same is true for many NURBS surfaces that define a shape. When you select a NURBS surface, the wireframe display on the surface shows the seam as a bold line. You can also find the seam by selecting the surface and choosing Display ➣ NURBS ➣ Surface Origins (see Figure 3.15).

The seam can occasionally cause problems when you’re working on a model. In many cases, you can change the position of the seam by selecting one of the isoparms on the surface (right-click the surface and choose Isoparm) and choosing Surfaces ➣ Move Seam.

NURBS Display Controls

You can change the quality of the surface display in the viewport by selecting the surface and pressing 1, 2,or 3 on the keyboard:

• Pressing the 1 key displays the surface at the lowest quality, which makes the angles of the surface appear as corners.
• Pressing the 2 key gives a medium-quality display.
• Pressing the 3 key displays the surface as smooth curves.

None of these display modes affects how the surface will look when rendered, but choosing a lower display quality can help improve performance in heavy scenes. The same display settings apply for NURBS curves as well. If you create a cubic curve that has sharp corners, remember to press the 3 key to make the curve appear smooth.

Lofting Surfaces

A loft creates a surface across two or more selected curves. It’s a great tool for filling gaps between surfaces or developing a new surface from a series of curves. In this section, you’ll create the bicycle seat from a series of curves.

1. Continue with the scene from the previous section, or open the bicycle_v02.ma scene from the chapter3scenes directory at the book’s web page.
2. Create a free image plane using the seat.jpg file from the chapter3sourceimages directory at the book’s web page. Transform the image plane roughly to match the scale and position of the seat in the front image plane. Use Figure 3.30 as a guide.

3. Starting a lofted surface from scratch can be daunting at first. The trick is not to worry about matching the shape. Instead, create a series of curves, loft the surface, and, through construction history, match the shape.

   Looking at the shape of the seat, you can estimate that you will need about eight control vertices to define the seat’s contours. Choose Create ➣ Curve Tools ➣ CV Curve Tool. Make sure that you are using a curve degree of 3. From the front viewport, draw a curve with eight CVs around the thickest part of the seat. Starting at the thickest point ensures that you will have enough CVs to define the surface accurately (see Figure 3.31).

4. Using multiple viewports, shape the curve roughly to match the outline of the seat. You are not going for accuracy. You just want to give the curve some shape in all three axes. Eventually, you will mirror the geometry since the seat is symmetrical. Therefore, the curve can start along the center line of the seat or on the XY plane. Also, plan on leaving the bottom open. Use Figure 3.32 as a guide.
5. With the curve selected, choose Edit ➣ Duplicate (or press Ctrl/Cmd+d) to make a standard duplicate of the curve.
6. Move the curve a unit in either direction.

7. Scaling the curve is a quick way to match the contour of the seat shape. The most effective way to scale the curve and maintain its position along the center line is to move the curve’s pivot point to its start.

   Hold D on the keyboard to enter pivot mode, and hold C to activate Snap To Curve. MMB-click the curve, and drag the pivot point to the start of the curve. Translate the curve to the top of the seat. Scale the curve in the y- and z-axes to match the height and width of the bicycle seat.

8. Repeat steps 5 through 7 to get a total of eight curves (see Figure 3.33).

   Leave the back of the seat open. It will be easier to close at a later time. Rotate the curve for the front of the seat 90 degrees.

9. Select the curves from front to back. The selection order dictates the direction of the surface as well as the lofting order. Selecting curves out of order will result in a loft that overlaps itself.
10. Choose Surfaces ➣ Loft ➣ ❒. In the Loft Options dialog box, make sure that the degree of the loft is set to Cubic.
11. Click the Loft button. Figure 3.34 shows the lofted surface.
12. With the basic surface created, you can now select individual curves and modify the shape interactively. To facilitate shaping the curves, add the surface to a referenced layer. You can also select all of the curves and press F8 to enter Global Component mode (see Figure 3.35). Global Component mode allows you to adjust the components of every object that you select instead of on a per-model basis.
13. Name the new surface seat. When you’re happy with the result, save the model as bicycle_v03.ma.

To see a version of the scene to this point, open the bicycle_v03.ma scene from the chapter3scenes directory at the book’s web page.

Attaching Surfaces

Once half of the model is shaped, you can mirror it to the other side and attach the surfaces together. The following steps take you through the process:

1. Continue with the scene from the previous section, or open the bicycle_v03.ma scene from the chapter3scenes folder at the book’s web page.
2. The construction history is no longer needed. Select the seat and choose Edit ➣ Delete By Type ➣ History.
3. Select all of the curves and delete them.
4. Select the seat. Choose Edit ➣ Duplicate Special ➣ ❒. Group the duplicate under World, and set Scale to −1.0 in the z-axis (see Figure 3.36). Make sure that the seat’s pivot point is located along the XY plane; you’ll scale from the pivot. Choose Duplicate Special to apply the settings and close the window.
5. Select the mirrored duplicate and original seat.
6. Choose Surfaces ➣ Attach ➣ ❒. You can choose from two different attachment methods. The first, Connect, will attach the two surfaces and preserve the existing shape. Blend will average the control vertices being attached. For the bike seat, choose Blend to create a smooth transition between the two surfaces. Uncheck Keep Originals and click Attach. Figure 3.37 shows the settings.
7. The two halves are now one. Notice that the front and back of the surface did not attach. This is because a NURBS surface must have four sides. Delete the node’s history and freeze its transforms.
8. You can continue to make adjustments to the surface to match the reference material by modifying its components. There are only two component types that you can manually adjust: hulls and control vertices.
9. Save the scene as bicycle_v04.ma.

To see a version of the scene to this point, open the bicycle_v04.ma scene from the chapter3scenes directory at the book’s web page.

Using Booleans

A Boolean operation in the context of polygon modeling creates a new surface by adding two surfaces together (union), subtracting one surface from the other (difference), or creating a surface from the overlapping parts of two surfaces (intersection). Figure 3.40 shows the results of the three types of Boolean operations applied to a polygon torus and cube.

Maya 2015 introduced a new carve library for its Boolean operations. The workflow is the same, but the results are improved. Regardless, Booleans are complex operations. The geometry created using Booleans can sometimes produce artifacts in the completed model, so it’s best to keep the geometry as simple as possible. It’s also beneficial to align the edges of one surface with that of another in order to reduce the number of extra divisions that may result.

In this section, you’ll use Boolean operations to weld the different parts of the bike frame together:

1. Continue with the scene from the previous section, or open the bicycle_v05.ma scene from the chapter3scenes folder at the book’s web page.
2. Select the two largest pipes of the bike frame. The ends of the pipes intersect each other by the handlebars. You can use an intersection to weld these two pipes together. Prior to performing the Boolean operation, the ends need to be cleaned up. Select the end vertices of both pipes (see Figure 3.41).
3. Open the options for the Scale tool by double-clicking its icon in the toolbox. The icon is a cube with four red arrows emanating from it.
4. Set the Step Snap to Relative and set the Step Size to 1.0. The Scale tool will now snap to a value of 1.
5. The goal is to make both ends flush with each other and to maintain the angle of the bottom pipe. Change the orientation of the manipulator by matching a point from the lower pipe. Under the Scale Settings rollout, click the triangle next to the xyz coordinate field. Choose Set To Edge. The selection is automatically set to edge in the viewport.
6. Select one of the horizontal edges from the top pipe. The manipulator aligns itself to the edge.
7. Scale the selection in the x-axis until the vertices are flush with each other. Figure 3.42 shows the result.
8. The open edges at either end of the pipes will prevent the Boolean from welding the two objects cleanly. The polygon faces that overlap will remain since neither surface is a closed volume. To close the ends, choose Mesh ➣ Fill Hole.

   

9. You can now use the Boolean tool on the two objects. With both surfaces selected, choose Mesh ➣ Booleans ➣ Intersection. It’s likely that both pipes will disappear after applying the Boolean. From the In-View Editor, choose Edge for the Classification. Figure 3.43 shows the results of the Boolean.
10. To bring the fork together with the large pipes of the frame, create a primitive polygon cylinder using the tool’s default settings, Create ➣ Polygon Primitives ➣ Cylinder.
11. Position the cylinder to match the reference material. Use the settings in Figure 3.44 to alter the construction history of the cylinder.
12. Before intersecting the parts, match up the geometry to avoid overlap and extra divisions. Scaling the ends of the pipe until the vertices reside inside the primitive cylinder works best. Use Figure 3.45 for reference.
13. It also helps if additional geometry is added to give the Boolean a better surface to cut into. Select the primitive cylinder, and choose Mesh Tools ➣ Insert Edge Loop.
14. Using the default settings of the tool, LMB-click the cylinder at the approximate location where the two frame pipes have been welded together (see Figure 3.46). Release the mouse button when you are happy with the edge loop’s placement.
15. Add two more edge loops on either side of the inserted edge loop. Align them with a corresponding edge from the frame. Use Figure 3.47 as a guide.
16. Select the frame, fork, and cylinder. The order is irrelevant. Choose Mesh ➣ Booleans ➣ Union. Figure 3.48 shows the result.
17. Delete the history, and save your scene as bicycle_v06.ma.

To see a version of the scene to this point, open the bicycle_v06.ma scene from the chapter3scenes directory at the book’s web page.

Cleaning Topology

Topology refers to the arrangement of polygon edges on a surface. The versatility of polygons allows you to alter components freely, which can result in bad topology. As a result, the polygons often require a bit of work to maintain their integrity. In this section, we’ll look at multiple tools for adding and removing polygon components.

1. Continue with the scene from the previous section, or open the bicycle_v06.ma scene from the chapter3scenes folder at the book’s web page.
2. The Boolean applied in the previous section has left numerous n-sided polygons and overlapping edges. You can clean these up quickly with the Target Weld tool. Choose Mesh Tools ➣ Target Weld. RMB-click the geometry and choose Vertex. A red circle shows up around the closest vertex to your mouse as a preselection highlight (see Figure 3.49).

3. The difference between a stray vertex and a vertex with good topology is that a stray vertex does not conform to the existing structure of the geometry. LMB-click a stray vertex, and drag to a vertex with good topology. A line is displayed between the two vertices.

   Notice how the good edges define the structure. Eliminating the vertices surrounding them will have little impact on the surface shape.

4. Work your way around the frame connection points. Only do one side or half of the geometry. Eventually, the clean side will be mirrored across. Figure 3.50 shows the bicycle frame after the stray vertices have been welded to existing vertices.

5. You can also eliminate the edges that are creating triangles on the surface. Having them gone will make modifying the surface easier and make the surface smoother, especially with smooth mesh preview (see Figure 3.51).

   There are two ways that you can delete an edge. The first is simply to select the edge and press Delete on the keyboard. The second is to select the edge and choose Edit Mesh ➣ Delete Edge/Vertex or press Ctrl+Delete. The difference between the two methods is that the latter will delete any non-winged vertices associated to the edge. Go through the area that you cleaned and remove the triangle edges. It should only be necessary to press Delete on the keyboard.

6. Use the Boolean tools for the rest of the bike frame and clean the topology. Add more cylinders as needed. Remember, you need to do only one side.

To see a version of the scene to this point, open the bicycle_v07.ma scene from the chapter3scenes directory at the book’s web page.

Creating Your Own Polygons

Primitives are a great place to start modeling, but some shapes are too irregular to make with primitives. You can build your own polygon shapes to begin a model. The following section walks you through the process of building the odd-shaped tire hanger of the rear tire.

1. Continue with the scene from the previous section, or open the bicycle_v07.ma scene from the chapter3scenes folder at the book’s web page. Half of the bike frame has been removed for simplicity.
2. Choose Mesh Tools ➣ Create Polygon.
3. Using the tool’s defaults, LMB-click to create the basic shape of the tire hanger. Leave out the round tab at the top-left corner (see Figure 3.52). When finished, press Enter to complete the shape.
4. When you’re building a round shape from scratch, there is no need to try to draw a circle. Instead, start with a primitive object, like a cylinder or sphere, to get a rounded object. You can then integrate the rounded shape into your object. For the tab, create a primitive cylinder.
5. Transform the cylinder to match the size and location of the screw hole in the tab. Use Figure 3.53 as a reference.
6. Select all of the faces of the cylinder except for one end. Press Delete to remove the geometry, leaving a polygonal disc (see Figure 3.54).
7. With the disc selected, choose Modify ➣ Center Pivot. The pivot point is forced into the middle of the disc.
8. Snap the disc to the XY grid plane. You can use the hot key x to snap to grid.
9. To complete the tab, RMB-click the geometry and select Edge. Double-click any of the exterior edges to select the entire outer loop.
10. Choose Edit Mesh ➣ Extrude. Extrude the edge selection to match the outer size of the metal tab (see Figure 3.55).
11. Delete the faces for half of the disc. Do not include any of the faces on the interior circle.
12. Select the border edges from the side of the disc that you deleted. You can select the row of edges by clicking the first edge and then double-clicking the last.
13. Choose Extrude. Do not move the extrusion. Choose the Move tool, and open its tool options. You want to translate the newly extruded edges in a linear direction that matches the center line of the disc. To do this, expand the Transform Constraint option menu and select Set To Edge from under the Move tool settings. Click the center edge. The Move tool updates to the new orientation.
14. Translate the edge selection to where it meets the polygon edge of the tire hanger, as shown in Figure 3.56.
15. Open the Scale tool options. Set the orientation of the Scale tool to the same edge from step 13. Scale the edge selection with a discrete scale of 1.0 to make the edges coplanar. Figure 3.57 shows the result.
16. You can now delete the interior faces that make up the hole of the tab. To select the faces quickly, RMB-click the geometry and choose Vertex. Click the center vertex of the interior disc. Ctrl+RMB-click the geometry and, from the marking menu, choose To Faces ➣ To Faces. Delete the selected faces.

To see a version of the scene to this point, open the bicycle_v08.ma scene from the chapter3scenes directory at the book’s web page.

Multi-Cut Tool

The Multi-Cut tool allows you to divide polygon faces. You can use it to make simple divisions, from one vertex to another, or to cut through multiple edges all at once. You are also allowed to draw divisions inside existing faces as long as you end up on an adjacent edge. The Multi-Cut tool effectively replaces the Interactive Split Polygon tool and the Cut Faces tool, and with the use of Ctrl and the Modeling Toolkit, you can also eliminate the Insert Edge Loop tool. To see the Multi-Cut tool’s fullest potential, watch MultiCut.mov in the chapter3movies folder at the book’s web page. Figure 3.58 shows an example of the Multi-Cut tool in action.

The following steps walk you through adding divisions with the Multi-Cut tool:

1. Continue with the scene from the previous section, or open the bicycle_v08.ma scene from the chapter3scenes folder at the book’s web page.
2. The tab and custom polygon shape need to be merged together. Before you can do this, their components must match. Select the custom polygon shape.
3. Choose Mesh Tools ➣ Multi-Cut. LMB-click the inside loop and then the outside edge to create a division. RMB-click to complete the division. You can also press Enter to complete the cut. Use Figure 3.59 as a guide.
4. Continue to add divisions to the surface. You need enough divisions, around six, to create a circular shape. The tire hanger has two circular shapes: one on the inside and one on the outside. Use the Multi-Cut tool to connect the two half-circles (see Figure 3.60).
5. Use the Multi-Cut tool to remove the remaining n-gons on the surface. You can click and hold an edge to drag the division along the length of the edge to be divided. Holding Shift snaps the division to 10-percent increments. Figure 3.61 shows the new divisions.

To see a version of the scene to this point, open the bicycle_v09.ma scene from the chapter3scenes directory at the book’s web page.

Combining and Merging Geometry

Typically it’s best to build complex parts as individual pieces and then bring them all together to form a single object. The tire hanger is made up of two separate pieces. To join them into one, you will use a combination of tools. The following steps take you through the process:

1. Continue with the scene from the previous section, or open the bicycle_v09.ma scene from the chapter3scenes folder at the book’s web page.
2. Select the tab and custom polygon shape. Choose Mesh ➣ Combine. The two separate objects are now a single node.

3. Delete the node’s history, and rename the node to tireHanger.

4. Select the four vertices that make up the center of the tab and polygon shape (see Figure 3.62).
5. Choose Edit Mesh ➣ Merge To Center.
6. Select the remaining vertices on one side of the tab. Use Target Weld to drag the entire selection to the left corner vertex of the custom polygon shape. Figure 3.63 shows the end result.
7. Repeat step 6 for the other side of the tab shape.
8. Shape the geometry to match the reference material. Save your scene as bicycle_v10.ma.

To see a version of the scene to this point, open the bicycle_v10.ma scene from the chapter3scenes directory at the book’s web page.

Bridge Polygon

The Bridge tool appends a series of polygons between border edges. The border edges must reside on the same node before the Bridge tool will work. The Bridge tool can make quick work of connecting the tire hanger to the frame of the bike. To use the Bridge tool, follow these steps:

1. Continue with the scene from the previous section, or open the bicycle_v10.ma scene from the chapter3scenes folder at the book’s web page.
2. Select the tire hanger. Extrude the geometry in the local z-axis to 0.1.
3. Center the object’s pivot. Snap the object to the center line of the frame, as Figure 3.64 shows.
4. To bridge between two objects, the border edges that you want to bridge must have the same number of edges. With the tireHanger node selected, choose Mesh Tools ➣ Multi-Cut ➣ ❒. The Modeling Toolkit opens.

   

5. Hold Ctrl and MMB-drag any edge along the thickness of the tire hanger (see Figure 3.65). The MMB forces the edge loop to be snapped along the center of the chosen edge. Release the mouse button to insert the loop.

6. Select the four faces next to the lowest bar on the bike frame and delete them. This creates a border edge. Use Figure 3.66 for reference.

7. Select the frame and tire hanger. Combine the objects into a single node.
8. RMB-click the object, and choose Edge from the marking menu.
9. Double-click both border edges, as shown in Figure 3.67.
10. Choose Edit Mesh ➣ Bridge. The defaults create too much geometry. In the In-View Editor menu, change Divisions to 1 (see Figure 3.68).
11. Repeat the steps 5 through 9, omitting step 6, to bridge the upper part of the bike frame. Figure 3.69 shows the finished product. Save your scene as bicycle_v11.ma.

To see a version of the scene to this point, open the bicycle_v11.ma scene from the chapter3scenes directory at the book’s web page.

Mirror Cut

The Mirror Cut tool creates symmetry in a model across a specified axis. The tool creates a cutting plane. Any geometry on one side of the plane is duplicated onto the other side and simultaneously merged with the original geometry.

In the options for Mirror Cut, you can raise the Tolerance, which will help prevent extra vertices from being created along the center line of the model. If you raise it too high, the vertices near the center may collapse. You may have to experiment to find the right setting.

1. Continue with the scene from the previous section, or open the bicycle_v11.ma scene from the chapter3scenes directory at the book’s web page.
2. Select the bike frame, and choose Mesh ➣ Mirror Cut ➣ ❒. Set Cut Along to the XY plane and choose Mirror Cut. A plane appears down the center of the bike frame’s geometry.

3. Set the Translate Z channel of mirrorCutPlane1 to 0.0. The mirrored geometry is extended.

   In the Outliner, several new nodes have been created. These include the mirrorCutPlane1 and the mirroredCutMesh1 group. The frame has been renamed to polySurface18 (see Figure 3.70).

4. Select the polySurface18 node, and choose Edit ➣ Delete By Type ➣ History. This removes the group nodes that were created. Select the mirrorCutPlane1 node, and delete it.
5. Name the polySurface18 node frame.

To see a version of the scene to this point, open the bicycle_v12.ma scene from the chapter3scenes directory at the book’s web page.

The rest of the bike can be modeled using the methods and techniques outlined in this chapter. When approaching a new piece, ask yourself if there is a primitive object that closely matches the surface shape or even a portion of the surface shape. For instance, the bike tire can be created quickly using a primitive polygon torus. You can use the following settings for the torus’s construction history.

• Radius: 6.21
• Section Radius: 0.52
• Subdivisions Axis: 30
• Subdivisions Height: 8

Figure 3.71 shows the finished version of the bike. You can also open the bicycle_final.ma scene from the chapter3scenes directory at the book’s web page.