Chapter 8 Polygon Meshes
From ShadeCamp
Polygon meshes are solid objects created by combining polygonal surfaces. As the vertices of a polygon mesh do not have tangent handles, moving the vertices enables you to transform objects. Since the features of polygon meshes differ from those of curved surfaces, you should consider which one to use for efficient modeling. In this chapter, you will learn to use polygon meshes.
Polygon Meshes
Polygon meshes are created by irreversibly converting curved surfaces, pseudo polygon meshes, multiple polygon meshes included in a part, or closed line objects with no tangent handles. Objects created with Boolean modeling and MetaMeshes are also considered polygon meshes. Polygon meshes are objects created by combining polygonal surfaces, which can have any structure without having to fulfill conditions for the lattice structure of curved surfaces. Control points of a polygon mesh do not have tangent handles. Multiple surfaces of a polygon mesh can share one vertex. Polygon meshes can be rendered with Smooth Shading. Polygon meshes can approximate curved surfaces by rounding the edges.
Converting to a PolygonMesh
To convert a curved surface, pseudo Polygon Mesh, or part containing multiple Polygon Meshes or quadrilateral or triangular closed line objects, select the part and choose Convert in the Toolbox. When a curved surface or pseudo Polygon Mesh is converted, the Division dialog box appears, allowing you to specify the number of subdivisions. If the Division dialog box appears, Enter the number by which the line objects displayed in the browser should be divided in the Division (Longitudinal) text box, and the number by which the line objects intersecting those line objects should be divided in the Division (Lateral) text box. The surface will be converted to a polygon mesh with the specified number of divisions.
If the object you selected to convert was not a curved surface or pseudo polygon mesh, the Convert to Polygon Mesh dialog appears, giving you a choice of several levels of surface subdivision.
A curved surface or pseudo Polygon Mesh can be transformed into a Polygon Mesh with a lattice structure by changing the number of line objects that subdivides them to a specified number. Parts containing multiple Polygon Meshes or closed line objects with no tangent handles are also transformed into Polygon Meshes. A Polygon Mesh can be modified without being restricted by the lattice structure.
Subdividing Polygon Meshes During Rendering
When the Round Edge value for a polygon mesh is set to 0, subdivision during rendering is not performed. When edges are rounded, fine subdivision is applied in accordance with the specified amount. For details about subdivision, refer to the “Subdividing Surfaces” section that appears later.
Changing Control Points
Surfaces can be modified at any time by changing control points with the Modify tool in the Toolbox. Surfaces can be added, deleted, or transformed by adding, deleting, or moving appropriate control points. Polygons with more than 5 planes (pentagon) will not be displayed as a surface when rendered.
The curved surface is transformed. Number of subdivisions is 32 x 9.
The control points are displayed.
Pseudo Polygon Meshes
A pseudo polygon mesh is created by irreversibly converting a curved surface. A polygon mesh is considered one means of converting a curved surface, which changes the number of line objects subdividing the curved surface to the specified numbers, deletes all tangent handles, and changes the surface’s name to “@” so that it will not be subdivided during rendering. The number of subdivisions in a curved surface is (u -1) x (v - 1), provided that the number of line objects forming the curved surface is u x v. The positions of anchor points after conversion will not be changed when the number of subdivisions remains the same. Otherwise, they are moved to positions interpolated by the program. A pseudo polygon mesh can be handled in exactly the same way as a curved surface.
To create a polygon mesh, select a curved surface or pseudo polygon mesh and click the convert button in the Toolbox while holding down the Ctrl (Win) / option (Mac).
The same curved surface from the previous section re-subdivided into 16 x 6.
The same curved surface from the previous section re-subdivided into 32 x 9.
The control points of the pseudo polygon mesh are displayed, which allow you to modify the object in terms of line objects.
Polygon Reduction
Because polygons can be added or deleted in bundles (units of line objects) after understanding the relative importance of the polygons in pseudo polygon meshes, they are extremely useful in reducing the number of polygons (referred to as polygon reduction). Ignore the restriction on number of polygons for the time being, and transform an object into a pseudo polygon mesh with the required accuracy; delete all unnecessary line objects at once, and transform it into a polygon mesh if required. This enables you to efficiently create a polygon model that partially retains the accuracy within the restriction of number of applicable polygons.
A curved surface that consists of nine open line objects and four closed line objects.
A polygon mesh created by directly subdividing the same figure into 12 x 8 surfaces.
The same figure which was first subdivided into a pseudo polygon mesh with 30 x 8 surfaces; then line objects which have relatively less effect on the characteristics of the object were deleted; and then the object was made into a polygon mesh with 12 x 8 surfaces.
Removing Wrinkles From a Curved Surface
Smooth shading can be set by applying Smooth in the Modify tool to a polygon mesh - that is an “@ “ part - then removing the “@” from the name. This technique may remove wrinkles on a curved surface resulting from inappropriate adjustment of tangent handles.
Editing Polygon Meshes
Polygon meshes can be modified using the Mesh Toolbox. Selecting View > Mesh Tools brings up a new toolbox containing all the Mesh tools. The Mesh Toolbox can also be displayed by clicking the Mesh button at the bottom of the standard Toolbox.
You must be in Modify mode to edit a polygon mesh. Select “Enter Modify Mode” from the Modify tool in the standard Toolbox, or press the “m” key to enter Modify mode.
Mesh Selection Mode
Polygon meshes can be modified by selecting their vertices, edges, or faces, and then using any of several editing tools. Clicking one of the three Mesh Selection buttons in the Mesh Toolbox (shown below) allows you to select and modify vertices, edges, or faces, respectively.
Vertex Selection mode;
Edge Selection mode;
Face Selection mode.
Selecting the vertices, edges, or faces of a polygon mesh is just like selecting control points.
For an explanation of how to select and edit control points, please see “Editing Line Objects” in the Shade User Guide, “Chapter 5: Creating Line Objects”.
Furthermore, the selected elements (either vertices, edges, or faces) are preserved even after switching to a different Mesh Selection mode. For example, if you select two adjacent vertices in the Vertex Selection mode, and then switch to Edge Selection mode, the edge connecting those two vertices will be selected. Likewise, if you select a face in Face Selection mode and then switch to Vertex Selection mode, the vertices composing that face will be selected.
In order to gain familiarity with the three selection modes, practice switching between them by following the examples below.
1. Choose “Rectangle” from the Create tool in the standard Toolbox, and make a rectangle similar to the one shown below.
2. If the Browser is not already visible, display it by choosing View > Browser.
3. With the rectangle selected, choose “Convert to Polygon Mesh” from the Convert tool in the Toolbox. The Convert to Polygon Mesh dialog box will appear. The Regular level of subdivision is fine for most purposes, so just click the OK button.
In the Browser, the rectangle (the part named “Closed line”) changes to “Polygon mesh”.
4. With the new polygon mesh selected, choose “Enter Modify Mode” from the Modify tool in the toolbox or press the “m” key to enter Modify mode.
5. If the Mesh Toolbox does not appear automatically, select View > Mesh Tools.
6. Click the Face Selection Mode button, in the top right corner of the Mesh Toolbox.
7. In the Figure window, click inside the rectangle (which is now a polygon mesh). The face of the rectangle will be selected.
8. Next choose “5” from the Divide tool (located on the left side toward the bottom of the Mesh Toolbox).
Shade divides the face into five rows and columns.
9. Now click the Deselect button in the Mesh Toolbox.
The rectangle’s face is deselected.
10. Click the Vertex Selection Mode button to switch to Vertex Selection mode.
11. Select several adjacent vertices as shown in the image below.
12. Now click the Edge Selection Mode button. The edges composed of the previously selected vertices become red (the default color) to show that they are selected.
13. In the same way, if you click the Face Selection Mode button, the faces composed of the previously selected edges now become selected.
14. Finally, click back on the Vertex Selection Mode button. The vertices composing the faces in Step 13 are now selected.
The vertex on the bottom left that was selected in Step 11 is no longer selected, because it was not part of any of the faces in Step 13.
Selection Tools
Here you will learn about the various tools available for selecting the vertices, edges, and faces of a polygon mesh. You will find that the ability to quickly and precisely select parts of a mesh will facilitate smooth, intuitive mesh editing.
Belt
To use this method first select two adjacent faces. By clicking the Belt button in the Mesh Toolbox, you automatically select all the faces forming a belt in the specified direction. When working with spherical meshes, the Belt tool is most effective in the latitudinal direction.
1. Create a sphere by choosing “Sphere” from the Create tool in the Toolbox.
2. If the Browser is not visible, display it by choosing “Browser” from the “View” menu.
3. Choose “Convert to Polygon Mesh” from the Convert tool in the Toolbox. When the Convert to Polygon Mesh dialog box appears, click OK. The sphere will be converted to a polygon mesh like the one in the following image.
4. With the polygon mesh selected in the Browser, enter Modify mode (from the Modify tool in the Toolbox).
5. If the Mesh Toolbox is not visible, click the Mesh button at the bottom of the standard Toolbox.
6. Click the Face Selection Mode button to enter Face Selection mode.
7. In the Figure window, select two adjacent faces of the mesh as shown below.
Now click the Belt button in the Mesh Toolbox. A `belt’ of faces is selected.
Loop
This method can be used if you have one or more faces selected, and want to edit the edges that form the outside boundary of those faces.
1. Create a polygon mesh out of a rectangle (closed line object) to look like the one below.
2. In the Figure window, select several faces, as shown.
3. Click the Loop button in the Mesh Toolbox. The edges bounding the previously selected faces are now selected.
Surface
This tool selects all the faces that share a common vertex with the currently selected faces.
1. Create a polygon mesh out of a rectangle (closed line object) to look like the one below.
2. In the Figure window, select a face as shown.
3. Click the Surface tool in the Mesh Toolbox. All the faces that share a vertex with the previously selected face become selected.
If a mirror copy or similar operation has been performed, the faces will look like they share vertices but actually do not. In such cases, the faces will not become selected through clicking the Surface button.
Detect
This tool is useful for finding and selecting areas of a polygon mesh that are causing artifacts to appear during modeling or rendering. The typical causes of artifacts fall into five categories: Overlapping Vertices, Overlapping Faces, Nonplanar Faces, Edge Shared by Multiple Faces, and Internal Faces. If you discover an undesirable artifact in your polygon mesh, try one or more of the following selection tools to troubleshoot the problem.
Overlapping Vertices
Overlapping vertices are two or more vertices that share the exact same coordinates in 3D space. If you find overlapping vertices, select them and then click the Merge Point button to merge the vertices.
1. Create a polygon mesh out of a rectangle (closed line object) to look like the one below.
2. In the Figure window, select a number of vertices as shown in the image below.
3. Verify that the “Snap” checkbox in the Toolbar is checked.
4. Choose “Uniscale” from the Move tool in the Toolbox. From the center of the object (in the figure below this is the origin), click and drag outward to the right as shown.
Click the Deselect button in the Mesh Toolbox to deselect the vertices.
6. Select “Overlapping Vertices” from the Detect button options. The center of the object will become selected to show the location of the overlapping vertices.
To remove the extra, overlapping vertices, click the Merge Points button in the Mesh Toolbox. The extraneous vertices are removed and the remaining vertext is selected.
To verify that the overlapping vertices have been removed, choose “Overlapping Vertices” again from the Detect tool. None of the vertices should become selected, showing that overlapping vertices no longer exist.
Select “Undo” from the “Edit” menu several times to revert the polygon mesh to its original state.
Overlapping Faces
Overlapping faces are two faces that share all the same vertices. If you find two overlapping faces, delete one of the faces.
1. With the rectangle polygon mesh from the previous exercise selected, open the Object Info window from the Aggregate palette. Check to make sure that the total number of faces and vertices are 25 and 36, respectively.
2. In the Figure window select the rightmost two columns of faces as shown below.
3. From the Mesh Toolbox click the Duplicate button.
4. In the Figure window, click on any empty space. The selected faces will be duplicated. You will not see the duplicate faces in the Figure window, but you can tell a copy has been made by looking at the Object Info window.
5. Now, the total number of faces and vertices displayed in the Object Info window should be 35 and 54, respectively.
6. Click the Merge Points button in the Mesh Toolbox.
The duplicate vertices are merged together.
After merging the vertices, the total number of vertices displayed in the Object Info window should return to 36. However, since the faces were not merged, their total number is still 35. Because of this, the two rightmost columns of the polygon mesh now have overlapping faces.
7. Choose “Overlapping Faces” from the Detect selection tool. The two rightmost columns of overlapping faces will be selected.
Press the delete key or choose Edit > Delete to remove the extra, overlapping faces. The overlapping faces are removed and the remaining faces become deselected. Also, the total number of faces shown in the Object Info window should return to 25, confirming that the Delete operation has been successful.
Choose Edit > Undo several times to undo the merge operation.
Nonplanar Faces
A nonplanar face is a polygon with vertices that do not all lie in the same flat plane. If you find a nonplanar face, you should move the problem vertices so that they lie in the same plane as the other vertices in the polygon.
1. In the Figure window, select a vertex as shown below.
2. Select “Translate” from the Move tool in the Toolbox, and drag the vertex up as indicated in the following image:
The four faces that share the vertex you moved have become nonplanar.
3. Choose “Nonplanar Faces” from the Detect button options in the Mesh Toolbox. The nonplanar faces become selected.
Moving the displaced vertex back down so that it lies in the same plane as the rest of the rectangle’s vertices will solve this problem.
4. Select “Undo” from the “Edit” menu to undo the move operation.
Edges Shared by Multiple Faces
Edges shared by multiple faces are edges that border three or more faces. If an edge shared by multiple faces is selected, delete it appropriately.
1. Open “UG_08_PolygonEdgeShare.shd” from the “Documentation - Sample” tab in ShadeExplorer.
In this file, three polygon meshes share an edge along the Z axis.
2. Select “Part” from the Part tool to create a new part.
3. In the Browser, move the three polygon meshes to inside the newly created part.
4. With the new “Part” selected in the Browser, choose “Convert to Polygon Mesh” from the Convert tool to combine the three polygon meshes into one.
By so doing, you merge the overlapping vertices, and the edge along the Z axis is now shared by three faces.
5. Choose “Edge Shared by Multiple Faces” from the Detect tool. The three faces that share an edge become selected.
From the Other tool in the Mesh Toolbox, select “Remove Edge Shared by Multiple Faces”. The faces that shared the edge are separated.
(This image shows that the faces can be moved separately after the problem edge is removed.)
Internal Faces
Internal faces are faces that were created inside a polygon mesh. If you find an internal face, delete it.
1. Open “UG_08_PolygonInternalFace.shd” from the “Documentation - Sample” tab in ShadeExplorer.
In this Shade scene, the inside faces of three polygon meshes overlap.
2. Create a new part by selecting the Part tool from the Toolbox.
3. In the Browser, move the three polygon meshes into the newly created part.
4. With the new “Part” selected in the Browser, choose “Convert to Polygon Mesh” from the Convert tool to combine the three polygon meshes into one.
The overlapping vertices are merged together, forming two faces that are completely enclosed within the polygon mesh.
5. Choose “Internal Face” from the Detect tool. The internal faces become selected.
To remove the internal faces, press the Delete key or choose “Delete” from the “Edit” menu.
Selecting Triangle, Square or Other Faces
Polygons with three side, four sides, or more than four sides can also be selected using the Detect tool. To select polygons with three, four or more sides you must be in Face Selection mode. Selected polygon faces are added to the current selection.
1. Open “UG_08_TrianglePolygon.shd” from ShadeExplorer.
2. With the polygon mesh selected in the Browser, from the Modify tool select Enter Modify Mode.
3. From the Detect tool, choose Select Triangle Faces.
The polygons with three sides are added to the current selection.
4. Now choose Select Square Faces from the Detect tool. The remaining polygon faces (all foursided) become selected.
Inverting the Selection
Clicking the Invert button will select the currently unselected vertices, edges, or faces (depending on the Mesh selection mode).
1. Convert a rectangle (closed line) to a polygon mesh as in the following image.
2. Click the Vertex Selection Mode button to enter Vertex Selection mode.
3. In the Figure window, select a number of vertices as shown below.
4. Click the Invert button in the Mesh Toolbox. The unselected vertices become selected, and vice versa.
5. If you click the Edge Selection Mode button, the edges become the selected elements, as in the following figure.
6. Click the Invert button once again. The selection is inverted.
7. Now enter Face Selection mode. The faces are now selected.
8. Clicking the Invert button again will switch which faces are selected.
Releasing the Selection
To release the currently selected vertices, edges, or faces, click the Deselect button.
Alternatively, you can hold Ctrl (Win) or Option (Mac) and click anywhere in the Figure window to release the selection.
Editing Tools
There are a variety of editing tools that can be used to modify the selected vertices, edges, or faces of a polygon mesh. By using a combination of tools you can create a complex object quickly and efficiently.
Offset
The Offset tool is used to enlarge or shrink a polygon face while keeping its position the same. It can also raise or lower the selected face. If you raise or lower a face with the Offset tool, the surrounding contiguous faces will be stretched such that they stay contiguous; no new polygon faces will be created. This can result in polygon faces that do not lie in a single plane. See “Nonplanar Faces” for information about nonplanar polygon faces.
After selecting a face and clicking the Offset tool, click and hold the mouse button over the selected face. A plus, minus, and two arrows (one pointing up and one pointing down) will appear, allowing you to drag the mouse like a joystick to manipulate the face. If multiple faces are selected, the Offset tool will manipulate them together.
1. Convert a rectangle to a polygon mesh, and divide it into five sections to look like the one shown below.
2. In the Figure window, select the five center faces as shown.
3. Click the Offset button.
4. Click and drag the mouse in the Figure window, using the virtual joystick that appears as a guide.
The selected face changes according to which direction you move the mouse:
Dragging up moves the face in the positive direction of the normal.
Dragging down moves the face in the opposite direction of the normal.
Dragging right enlarges the face while keeping its position the same.
Dragging left shrinks the face while keeping its position the same.
Releasing the mouse button while the cursor is in the center of the virtual joystick cancels the Offset operation.
Drag the mouse in the positive direction (to the right). The selected faces are enlarged.
Extrude
The Extrude tool will extrude a face in the positive or negative direction of the normal. Unlike the Offset tool, using the Extrude tool to extrude a polygon face will create new faces composing the sides of the newly extruded face. Thus, if you have a flat polygon mesh in the X-Z plane consisting of nine contiguous polygon faces, extruding one of these faces in the Y direction will result in a polygon mesh of thirteen (the nine original plus four new) polygon faces. If multiple faces are selected, the Extrude tool will extrude them together, as if they were one polygon.
1. Create a sphere and convert it to a polygon mesh.
2. Click anywhere in the Perspective view, and then select Rendering > Display Mode > Shading + Wireframe. This will make it easier to see the result of the Extrude operation.
3. Enter Modify Mode, and in the Figure window select several polygon faces as shown in the following image.
4. Click the Extrude button in the Mesh Toolbox.
If you then click in the Figure window, the virtual joystick will appear.
The selected face changes according to which direction you move the mouse:
Dragging up extrudes the face in the positive direction of the normal.
Dragging down extrudes the face in the opposite direction of the normal.
Dragging to the right enlarges the face while keeping its position the same.
Dragging to the left shrinks the face while keeping its position the same.
Releasing the mouse button while the cursor is in the center of the virtual joystick cancels the Extrude operation.
6. Drag the mouse upwards. The selected faces are extruded.
Bevel
The Bevel tool is similar to the Extrude tool, except that when multiple faces are selected, each face is beveled separately, following its respective normal. When modifying a single polygon face, the Bevel and Extrude tools function identically.
1. Convert a sphere to a polygon mesh as in the following image.
2. Change the display mode to “Shading + Wireframe” (in the “Rendering > Display” menu).
3. In the Figure window, select several contiguous faces.
4. Click Bevel in the Mesh Toolbox.
5. Click and hold the mouse button in the Figure window to make the virtual joystick appear.
The selected face changes according to which direction you move the mouse:
Dragging upwards bevels (extrudes) the face in the positive direction of the normal.
Dragging downwards bevels (extrudes) the face in the opposite direction of the normal.
Dragging to the right enlarges the face while keeping its position the same.
Dragging to the left shrinks the face while keeping its position the same.
Releasing the mouse button while the cursor is in the center of the virtual joystick cancels the Bevel operation.
Drag the mouse upwards. The selected faces are each beveled outwards separately. Notice that each of the beveled faces only touch each other at their edges on the surface of the sphere, in contrast to the results of the Extrude operation.
Duplicate
The Duplicate tool allows you to first copy the selected polygon faces, and then move, extrude, enlarge or shrink the duplicate faces.
1. Convert a rectangle to a polygon mesh and divide it into five rows and columns with the Divide tool.
2. In the Figure window, select the two columns of polygons on the right.
3. Click the Duplicate button.
4. Click and hold the mouse button in the Figure window to make the virtual joystick appear.
The selected faces are duplicated, and the duplicate faces change according to which direction you move the mouse:
Dragging upwards copies and moves the faces in the positive direction of the normal.
Dragging downwards copies and moves the faces in the opposite direction of the normal.
Dragging to the right copies and enlarges the faces while keeping their position the same.
Dragging to the left copies and shrinks the faces while keeping their position the same.
Releasing the mouse button while the cursor is in the center of the virtual joystick cancels the Duplicate operation.
5. Drag the mouse upwards. The selected faces are copied and the duplicates moved upwards.
Detach
This tool detaches the selected faces from its surrounding contiguous faces. Although the face is separated from its adjacent faces, it still belongs to the same polygon mesh. In other words, the Detach tool does not split the polygon mesh into two meshes. In a similiar fashion to the Duplicate tool, the Detach tool can move, enlarge, or shrink the detached face(s).
1. Convert a rectangle to a polygon mesh and divide it into five rows and columns using the Divide tool.
2. In the Figure window, select the two columns of polygons on the right.
3. Click the Detach button in the Mesh Toolbox.
4. Click and hold the mouse button in the Figure window to make the virtual joystick appear.
The selected faces change according to which direction you move the mouse:
Dragging upwards detaches and moves the face in the positive direction of the normal.
Dragging downwards detaches and moves the face in the opposite direction of the normal.
Dragging to the right detaches and enlarges the face while keeping its position the same.
Dragging to the left detaches and shrinks the face while keeping its position the same.
Releasing the mouse button while the cursor is in the center of the virtual joystick cancels the Detach operation.
5. Drag the mouse upwards. The selected faces are detached and moved upwards.
Mirror Copy
With this tool you can create a mirror copy of a polygon mesh face along any axis. The mirror copy will become part of the original polygon mesh.
1. First convert a sphere to a polygon mesh.
2. Next, choose Translate from the Move tool and move the sphere so that its leftmost point is just touching the origin.
3. Select all the faces of the sphere (polygon mesh). The easiest way to do this is to click the Invert button in the Mesh Toolbox when none of the faces are selected.
4. Now click the Mirror Copy button.
The mirror copy is made along the axis of your choice, as described in the following step. In this example, the cursor is positioned over the origin.
5. Click and hold the mouse button at the point you wish to designate as the axis for the mirror copy. Drag the mouse in the direction you want to insert a copy. In this case, the mouse is dragged to the left, and the sphere to the right of the axis is copied to the left.
6. Choose Edit > Undo to undo the mirror copy operation.
7. Create another mirror copy by clicking the Mirror Copy button again and placing the mouse at the origin.
8. This time, click and drag the mouse in an arc away from the invisible axis. The mirror copy of the sphere rotates about the axis.
A mirror copy created without dragging the mouse at all will create a copy of the selected object at the same position as the original.
Copy
The Copy tool allows you to create a copy of an existing polygon mesh object as a new polygon mesh. The Copy tool can also be used to copy multiple separate polygon meshes and merge them to create one new polygon mesh.
Copying a Single Polygon Mesh
Convert a rectangle to a polygon mesh, and divide it into five rows and columns.
Select the two rightmost columns of faces.
Click the Copy button in the Mesh Toolbox. The selected faces are copied as a new polygon mesh in the same location as the original. You can then independently manipulate the new polygon mesh however you like.
Copying Multiple Polygon Meshes
1. Convert a sphere to a polygon mesh.
2. Choose Copy from the standard Toolbox, and translate the second sphere so that it is adjacent to the first. In the Browser, you should see that there are now two polygon meshes.
In the Figure window, in Face Selection mode, select the front half of each of the spheres as shown in the figure below.
Click the Copy button in the Mesh Toolbox. The selected faces are copied together as one new polygon mesh located in the same position as the original two polygon meshes. You can now modify this new polygon mesh independently from the original two polygon meshes.
Knife
1. Convert a rectangle to a polygon mesh, like the one shown below.
2. In the Figure window, select the face of the rectangle.
3. Click the Knife button in the Mesh Toolbox.
4. Now click and drag the mouse across the face, forming a diagonal line as shown in the image below.
5. The face is cut into two pieces along the line you drew.
Divide
The Divide button is used to split the selected face into equal horizontal and vertical segments.
1. Convert a rectangle to a polygon mesh.
2. In Modify mode, click the Face Selection Mode button, and select the face.
3. Choose the “5” option from the Divide tool. The selected face is divided into five equal horizontal and vertical segments.
Dividing into Triangles
1. Convert a rectangle to a polygon mesh.
2. Select the face of the polygon in the Figure window.
3. Choose Triangle from the Divide tool. The selected face is divided into two triangular faces.
Align
The Align tool is mainly used to align the position of the selected vertices along a specified direction (right, left, top, bottom, front, or back). The aligned vertices form a plane that includes the vertex farthest away from the object. The Align tool also has options to align to a straight line, weld vertices and unify the normals of the polygons.
1. Convert a sphere to a polygon mesh as shown in the following image.
2. Enter Modify mode, and click the Vertex Selection Mode button in the Mesh Toolbox to enter Vertex Selection mode.
3. In the Figure window, select the vertices in the right half of the sphere as in the figure below.
4. Click the Align tool and choose “Align right.” The selected vertices are all repositioned to align with the rightmost vertex.
Note: You can also use the Align tool when edges or faces of a polygon mesh are selected. The result will be the same as if the respective vertices were selected.
Align to Straight Line
1. Convert a rectangle (closed line) to a polygon mesh and divide it into several sections using the Divide tool as shown:
2. Click the Vertex Selection mode button to enter Vertex Selection Mode.
3. In the Figure window, select the following vertices in order from 1 to 5:
4. Choose Align to Straight Line from the Align tool in the Mesh Toolbox. The vertices all align to an imaginary line drawn between the first and last selected points.
Weld Vertices
1. Create a Sphere and convert it to a polygon mesh.
2. Click the Vertex Selection mode button to enter Vertex Selection Mode.
3. First select the vertex shown as “1” in the figure below. Then select all the vertices in the right half of the sphere when viewed in the Front view.
4. Choose Weld Vertices from the Align tool in the Mesh Toolbox. The selected vertices are welded to the single point you first selected.
Unify Normals
1. Open “UG_08_NormalLine.shd ”from ShadeExplorer.
2. Select the polygon mesh in the Browser and press the “m” key to enter Modify Mode. Notice that the normal lines of the polygons are displayed. You can show or hide the normals of a polygon mesh by choosing Show Normals (or Hide Normals) from the Modify tool in the standard Toolbox.
3. If you look in the Front or Side views, you can see that some normal lines are pointing up and some are pointing down. This means that the polygons are not all facing the same direction.
4. Select all the polygon faces and choose Unify Normals from the Align tool. All the normal lines no face up.
Merge Face
This button merges the faces of two or more adjacent polygons. Vertices and edges shared by the faces will be deleted after they are merged.
1. Convert a rectangle to a polygon mesh and use the Divide tool to divide it into five rows and columns.
2. With the polygon mesh selected in the Browser, choose View > Object Info to open the Object Info window.
3. Verify that there are a total of twenty-five faces in the Mesh.
4. In the Figure window, select all the polygon faces.
5. Click the Merge Face button. The selected faces are merged into one face.
6. In the Object Info window, verify that the total number of faces is now one.
7. Choose “Undo” from the “Edit” menu to undo the Merge Face operation.
8. Now select the faces as shown below:
9. Click the Merge Face button again.
Each group of contiguous of polygon faces is merged separately.
10. The total number of faces shown in the Object Info window is now only nineteen.
Merge Point
The Merge Point tool is used to merge two vertices that share the same 3D coordinates.
1. Convert a rectangle to a polygon mesh and divide it into five rows and columns as before.
2. With the Mesh selected in the Browser, open the Object Info window.
3. Check that the total number of vertices is thirtysix.
4. In Face Selection mode, select the two rightmost columns of polygons.
5. Click the Copy button in the Mesh Toolbox, and click somewhere in the Figure window. The selected faces will be copied inside the same polygon mesh, at the same location as the originals.
6. Looking in the Object Info window, you can see that there are now a total of fifty-four vertices.
7. Now choose Translate from the Move tool in the Toolbox, and drag the selected faces to the right, as shown below.
The right edge of the original polygon mesh and the left edge of the copied polygon mesh are now overlapping perfectly. The vertices that form these edges occupy the same respective coordinates.
8. Click the Merge Point button in the Mesh Toolbox. The overlapping vertices are merged together.
9. In the Object Info window, you will see that the total number of vertices has changed to forty-eight.
Flip Face
The Flip Face button inverts the normals of the selected faces. You might call this turning the polygons inside out (or vice versa).
1. Convert a rectangle to a polygon mesh and divide it into five rows and columns.
2. In the Figure window, select the center faces as shown in the following image.
3. Choose “Show Normals” from the Modify tool in the Toolbox. The normals of each face appear. You can see that they are all pointing up.
Click the Flip Face button in the Mesh Toolbox. The selected faces are flipped, and the normals now point down.
Choose “Shading + Wireframe” from “Display Mode” in the “Rendering” menu. This will make it easy to distinguish between the front and back sides of the polygons.
Click the Deselect button from the Mesh Toolbox to release the selection, and then choose “Single-sided” from the “Rendering” menu. The faces that were flipped are not shaded, since we are now looking at their backsides.
Face
This tool creates a face between the selected vertices.
1. Convert a rectangle to a polygon mesh, and divide it into five rows and columns.
2. To make it easy to see the faces, switch the Display Mode to Shading + Wireframe from the contextual menu.
3. Select the center nine faces as shown below.
4. Delete the selected faces.
5. Click the Vertex Selection Mode button in the Mesh Toolbox to enter Vertex Selection mode.
6. Select the inside vertices as shown below.
7. Click the Face button. A new polygon face is created between the selected polygons.
The newly created face is automatically assigned a front and back side.
Note: If the face is not facing the direction you want, click the Invert button in the Mesh Toolbox.
Subdivision
This tool sets the surface subdivision of the selected polygons. This determines the degree to which the corners will be rounded. Clicking this button toggles the Roundness slider in the Object Info window between 0 and 1.
1. Convert a rectangle to a polygon mesh.
2. Enter Modify mode.
3. Switch the Display Mode to Shading + Wireframe from the contextual menu to make the face more visible.
4. With the polygon selected, open the Object Info window.
5. Check to see that the value of the Roundness slider is set to 0.
6. Click the Subdivision button in the Mesh Toolbox. The value of the Roundness slider changes to 1, and the corners of the polygon mesh are rounded.
However, note that in the Shading preview mode we can’t see that the corners are perfectly round.
7. Open the Rendering Settings window from the “Rendering” menu.
8. Click on the Basics tab, and set the surface subdivision to “Very fine”. Click the Render button to start rendering. The rendered image shows that the corners are rounded.
9. Click the Subdivision button in the Mesh Toolbox again. The Roundness slider value returns to 0 and the corner rounding disappears.
Removing Edges Shared by Multiple Faces
This option is located within the Other button submenu in the Mesh Toolbox. If there are any edges shared by three or more faces in the selected polygon mesh, choosing this option will separate the faces concerned so that they no longer share the exact same edge. If there are no edges shared by three or more faces in the selected polygon mesh, this option has no effect.
Note: For more information, see “Edges Shared by Multiple Faces.”
Select Plane
Choosing this option will select all of the polygon faces lying in the same plane as the currently selected face.
The following is an example of how to use the Select Plane option.
1. From ShadeExplorer, open the file “UG_08_PolygonFlatness.shd” from ShadeExplorer.
2. In the Figure window, enter Modify mode and select one of the top faces.
3. Choose “Select Plane” from the Other button of the Mesh Toolbox. All of the adjacent faces lying in the same plane as the selected face become selected. In this example, this includes all the faces in the top surface of the polygon mesh.
4. Click the Vertex Selection Mode button, and the selection switches to show only the vertices.
5. Select several vertices forming a square, such as the nine vertices in the left corner of the polygon mesh’s top surface, as shown in the figure below.
6. Choose “Rotate” from the Move tool in the Toolbox, and rotate the selected vertices slightly about the center.
7. Switch back into Face Selection mode.
8. Select two polygon faces: one of the original unmodified faces and one of the faces that you just rotated.
9. In the Mesh Toolbox, choose “Select Plane” from the Other button. In this case the faces in two separate planes become selected.
Note: When working with a sphere this option will have no effect, as none of the faces of the sphere lie in the same plane.
Extrude + Move
This option from the Other button’s submenu allows you to extrude and move a face at the same time.
1. Extrude a rectangle to form a cube, and then convert it to a polygon mesh.
2. In the Figure window, select one side of the Mesh as shown.
3. Choose “Extrude + Move” from the Other button of the Mesh Toolbox. Next, click and drag the mouse in the Figure window. The face is extruded and moved in the direction that you drag.
Extrude Edge
With the Extrude Edge option you can extrude an edge to form a new polygon face. This option is located within the Other button submenu in the Mesh Toolbox.
1. Convert a rectangle to a polygon mesh and divide it into five rows and columns as shown.
2. Click the Vertex Selection Mode button to enter Vertex Selection mode.
3. In the Figure window, select several edges in a straight line along one side of the polygon mesh, as shown in the figure below.
4. Choose “Extrude Edge” from the Other button in the Mesh Toolbox, and click and drag the mouse away from the polygon mesh. The selected edges are extruded in the direction you dragged, and a new face is created.
Swap Triangle
This option is accessible from the Other button in the Mesh Toolbox.
1. Open “UG_08_TrianglePolygon.shd” from the Documentation - Sample tab in ShadeExplorer.
2. Select three of the polygon edges in the Figure window as shown here:
3. Choose Swap Triangle from the Other button in the Mesh Toolbox.
Using the Virtual Joystick
The following tools in the Mesh Toolbox utilize a virtual joystick to achieve the desired effect: Offset, Extrude, Bevel, Duplicate, Separate.
The basic operations of the virtual joystick are the same for all these tools. The greater the distance you move the mouse away from the center of the virtual joystick, the greater the distance the actual vertex, edge, or face will move.
Moving in the Direction of the Normal
By clicking and dragging the mouse in the direction, you can move the selected vertex, edge, or face in the positive direction of the normal.
Moving in the Opposite Direction of the Normal
By clicking and dragging the mouse in the direction, you can move the selected vertex, edge, or face in the negative direction of the normal.
Enlarging the Face
By clicking and dragging the mouse in the direction, you can enlarge the selected face. Its position in the polygon mesh does not change.
Shrinking the Face
By clicking and dragging the mouse in the direction, you can shrink the selected face. Its position in the polygon mesh does not change. The minimum size to which a face can be shrunk is to a point of 0 area.
Multiple Operations
By clicking and dragging the mouse diagonally across the virtual joystick, the actions associated with the respective directions will take effect simultaneously. For example, by dragging the mouse up and to the left (in the and directions), the face is extruded upwards and shrunk to a smaller size at the same time.
Using the Center of the Virtual Joystick
By releasing the mouse button in the center of the virtual joystick, the following effects take place:
Offset: The face doesn’t change.
Separate: The face is separated at its current location.
Bevel, Extrude, Copy (tools that create a new face): The new face is created at the same position as the selected face. The Bevel and Extrude tools create a face of 0 area in the same position as the |
