"Triangles"

David Sharp mailto:dsharp@interport.net

Here is a link to the web version of this page:www.oocities.org/Athens/Academy/8764/triangles.htm

Download (latest version: March 23, 2000)

Source code to Triangles
Source code posted here will usually be about two updates behind, until the development gets more stable. To compile (without modification of the code) you need to have installed DJGPP and the Allegro game library.

• About/Disclaimers
• Setting Up
• Using Triangles
  • Wire-frame view mouse operations
    • Create vertex
    • Select vertex
    • Select in rectangle
    • Select connected component
    • Move mesh
    • Mouse moVe
    • Translating mesh
    • Pull vertex
    • Pull edges
    • Repulsive mouse
    • Rotate mesh
    • Scale mesh
    • Insert vertex
    • Delete vertex
  • 3d view mouse operations
    • Rotate
    • Pan
    • Scale
  • Files
    • Load
    • Save
    • Save As
    • Get Undo
    • Quit
  • Editing operations
    • Make triangle
    • Delete triangle
    • Duplicate
    • Copy
    • Paste
    • Reflections
    • Delete Selected
    • Meld
    • Extrude
    • Marking
    • Select All
    • Snap to grid
    • Invert Selection
    • Remove loose vertices
    • Meld coincident vertices
    • Orient
    • Evert orientations
    • Divide, Smooth, Reduce, Deform
      • Subdivide
      • Smooth subdivide
      • Reduce
      • Deformations
        • Repulsive Point
        • Roughen
        • Wave
        • Ripple
        • Twists
        • Bend
  • Options menu
  • Polygons
    • Triangulate polygon
    • Lathe polygon shape
    • Pipe

Triangles is meant for modeling objects, not for producing images. It intended use is for making objects to be rendered using POV-Ray ray-tracing program. There is an upper bound on the number of triangles allowed (currently 50,000), so its main value is for modeling 'objects' rather than entire scenes. Even given the narrow niche Triangles is meant to fill, it is still missing many valuable features and I can't say that development will continue beyond what I personally need.

Setting up
Create a directory for Triangles. Unzip the downloaded zip file into this directory. To use under Windows, double click on the Triang.exe icon in Windows Explorer (or File Manager, or whatever), or get a DOS prompt and run Triang.exe. To use under plain DOS (not shelled to DOS from Windows), it is necessary to have the file CWSDPMI.EXE in your 'PATH', or in the directory you are running Triangles from. You will need to have video supporting 'at least' 640x480 pixels and 256 colors. You can set the video resolution to a few different settings using the Options Menu after Triangles starts. To have Triangles start up in a particular resolution (640x480, 800x600, 1024x768, 1200x1024, or 1600x1200), modify the file 'triangles.ini'. It must have one of the above copied literally into the first line of the file. To have Triangles always start in 1024x768, for example, modify (or create) the ASCII text file named 'triangles.ini' so that the first line is
1024x768
and make sure that your 'triangles.ini' is in Triangles's working directory.

Using Triangles
There are four view windows to see what you are doing. Three wire-frame views, and one '3-d' view. The wire-frame views are not adjustable (zooming or panning), but you can easily scale, rotate, or move your mesh around to get an appropriate view. The 3-d view presently uses the simplest "painter's algorithm" for rendering, and it can sometimes create false impressions, like triangles which seem to disappear when rotating, especially when the edge angles are large. Once the mesh has been smoothed some, the weirdness usually goes away. I may eventually add z-buffering to eliminate the problem, but maybe not.

Command Line
The Triangles command line can take the name of a TRI or RAW file to start up with. (This allows you to 'drag and drop' a file onto a Triangles icon). e.g.:
C:\Triangles>Triang.exe myfile.tri
would start Triangles with the file 'myfile.tri'.

Another command line option is how much memory to allocate for meshes. '-mN', where N is an integer, will make room for Nx1000 vertices, Nx1000 triangles, and 2N*1000 edges. e.g.:
C:\Triangles>Triang.exe -m100
would start Triangles with room for 100,000 vertices, 100,000 triangles, and 200,000 edges. The default (without using the command line option) is 50,000 vertices.

Mouse
The right mouse button in any of the three wire-frame view windows brings up a menu of "mouse choices". This is a list of things you can have the mouse do in the wire-frame views:

• After choosing "Create vertex ('c')", clicking in one of the wire-frame views will create a new vertex under the mouse's position. The created vertex is "selected" (and shown green). A "plain" left click (no CTRL key held) will unselect everything but the new vertex (so that all the green highlighting gets transferred to the new vertex). To have a new vertex added to whatever is already selected instead, use CTRL-left-click (hold down the Control key while clicking the left mouse button) in creating the vertex.
• "Select vertex ('s')" will cause the vertex (or vertices) directly under the mouse cursor to be selected when the mouse is left-clicked. A plain left click unselects everthing else. A CTRL-left-click will add the vertex (or vertices) under the mouse to the ranks of the "selected vertices", if that vertex is not already selected, or unselect it if it is already among the selected.
• "Unselect vertex ('u')", naturally, causes vertices left-clicked on to be removed from the selected vertices.
• "select in rectanGle ('g')" is for 'drag-drawing' a rectangle in a wire-frame view. Any vertices inside the drawn rectangle when the left button is released become selected. If the CTRL key is held down during this rectangle drawing, the vertices inside the rectangle are added to those already selected, otherwise everything outside the rectangle becomes unselected.
• "unselect in rectanGle ('Alt-g')" unselects any vertices inside a drawn rectangle.
• "selecT connecTed componenT ('t')" selects all vertices connected by triangle edges to the clicked-on vertex. Holding down the <Ctrl> key while clicking on a vertex will add those connected vertices to whatever is already selected.
• "unselecT connecTed componenT ('alt-t')" unselects all vertices connected by triangle edges to the clicked-on vertex.
• Dragging the mouse in a wire-frame view while "Move selected ('m')" ("Move all ('Alt-m')") is in effect moves the selected (all) vertices with the mouse. (Restrict the movement to either horizontal or vertical directions by holding down a Shift key while moving the mouse).
• "mouse moVe ('v')" is for clicking on a single vertex and dragging it with the mouse. (Restrict the movement to either horizontal or vertical directions by holding down a Shift key while moving the mouse). While mouse moVe is in effect, if you move a vertex 'on top' of another (one on top of other in the current wire-frame view), and right-mouse-click while the left-button is still held down, the two vertices will meld into one and can be used as a 'manual' mesh size reducer
• "Pull selected ('p')" and "Pull all ('Alt-p')" are similar to mouse moVe, but drag the selected (or all) vertices along. The further away from the dragged vertex any particular vertex is, the less strongly it is pulled. Under the Options Menu, Pull can be adjusted. Higher values reduce the effect on distant vertices, and lower values (closer to zero) increase the dragging effect on distant vertices. (Distance is through 'space', not through edges. A vertex sitting near the pulled vertex will be pulled strongly, whether or not the two are connected)
• "Pull edges ('p')" is like 'Pull all', but the distance of vertices from the 'pulled' vertex is calculated by following the edges connecting the vertices. Vertices which are not connected to the pulled vertex through any sequence of edges are not pulled at all. With meshes larger than even 100 vertices, the time needed for the calculation of distances is a real hindrance, so you can set (under the Options Menu) the maximum number of edges through which the pull effect will travel. Setting 'Max Edges' to a larger value means vertices farther away will be pulled, but the required calculation times go up quickly!
• "repulsive mouse ('h')" pushes vertices away from (or towards) the mouse position,
  X_new=X + c * (X-M)*e^{-a*(||X-M||^b)}
  where X is a vertex position, and M is the mouse's position. Pushes points of the mesh away from (c>0) or towards (c<0) the mouse. Mesh vertices closer to the mouse are pushed/pulled more. Set the parameters a, b, and c in the box that pops up on selecting 'repulsive mouse'. Note that these parameters are the same ones used for 'Repulsive point' (Edit->Deform->Repulsive point), and the settings for a, b, and c persist into Repulsive point.
• Dragging the mouse in a wire-frame view while "Rotate selected ('r')" (Rotate all ('Alt-r')") is in effect rotates the selected (all) vertices in the viewing plane of the view where you start the mouse dragging. The amount and direction of the rotation are determined by the arc the mouse makes about the center of the view window, (so dragging the mouse through an arc further from the center of the view window gives more control)
• "scaLe selected ('L')" ("scaLe all ('Alt-L')") lets you change the size of the triangle mesh by dragging the mouse. If the "scale uniformly" box is checked in the Options Menu, then all dimensions of the mesh will be scaled at the same rate. If scale uniformly is not checked, the scaling is only in the directions of the axes corresponding to up/down or left/right in that particular wire-frame view.
• "Insert vertex ('Alt-I')" finds the edge nearest where the mouse is clicked, and inserts a new vertex connecting the endpoints of that edge, making new triangles as necessary.
• The "Delete vertex ('d')" menu item enables clicking on a single vertex to delete it. Deleting vertex also removes from the mesh any triangles the vertex is a corner of.

The right mouse button in the "3-d" view window brings up a menu of 3-d view "mouse functions". Note that rotations, translations, and scalings in the 3-d view have no effect on the actual mesh. That is, they should be considered as changing your viewpoint, not moving or rotating the mesh.

• Picking Rotate (1) or Rotate (2) cause dragging the mouse in the 3-d view to rotate your view around the mesh.
• Picking a Pan causes dragging the mouse in the 3-d view to move your viewpoint left, right, up, down, in, or out.
• Scale makes the mesh appear larger or smaller.

File menu

• Load
  Load a mesh from either a TRI file or RAW triangle mesh file. TRI files are Triangle's in own particular ASCII format. The first line reads
  vertices
  followed by a list of vertex coordinates one x, y, z triple per line. Then the 'keyword'
  triangles
  followed by a list of triangles, three vertex indices per line. Here is a how a square looks in a TRI file:

  ---

  vertices
  -100.0,  100.0,  0.0   # coordinates of vertex 0
   100.0,  100.0,  0.0   # coordinates of vertex 1
   100.0, -100.0,  0.0   # coordinates of vertex 2
  -100.0, -100.0,  0.0   # coordinates of vertex 3
  triangles
  0 1 2   # first triangle's corners
  0 2 3   # second triangle
  

  ---

  
  A couple things to note when loading a RAW file into Triangles: 1) "Smooth RAW" files can be loaded, but normals and other info given in the file are not used by the program (and are not saved). 2) Any two vertices which are in exactly the same place are combined into one vertex.

• Save
  Save the current mesh as a TRI file.
• Save seLection
  Saves only the selected vertices together with whatever triangles they may completely define as a TRI file.
• Save As
  Gives a choice of formats to save in. currently these are:
  • TRI, Triangles's own format
  • POV-Ray triangle mesh
  • POV-Ray smooth_triangle mesh
  • (Mega)POV mesh2 (flat)
  • (Mega)POV mesh2 (smooth)
  • PCM file (A special format for POV-Ray 3.1 using Chris Colefax's "Compressed Mesh Macro" include file ("PCM.MCR")
  • PCM smooth mesh
  • RAW triangle mesh
  • RAW smooth triangle mesh
  When saving POV-Ray or RAW triangle meshes, you can choose to save different connected components as different meshes. For POV-Ray files, this will make a separate mesh{} (or MegaPOV mesh2()) object for each component. For RAW files, this just separates components in the file and inserts a 'name' ('COMPONENT1', 'COMPONENT2', etc) in front of each component (this is valuable mainly for converting files to other formats). When saving as POV mesh or mesh2 objects, you can choose to insert a texture into the mesh component. This inserts a 'place holder' texture named TEXTURE1, TEXTURE2 (etc) at the end of each mesh definition. These 'place holder' textures will need to be defined in your .POV file before #including or using the mesh. Also, when saving as POV mesh, opting to 'declare extents' will insert #declare statements of the minimum and maximum x, y, and z coordinates for each mesh. For example, if component 2's lowest point had y coordinate -20.56, the line
  #declare COMPONENT2_MIN_Y = -20.56;
  will be in the saved .INC or .POV file so that you can use these in your scene file.
• Get Undo
  Before doing deformations, reductions, divisions, or quitting the program, a copy of the mesh is saved to the file "lasttri.tri". Get Undo just retrieves and loads this file. This will retrieve the mesh from just before the last deformation, or from the end of the last session. It is not a general 'undo'.
• Quit
  Quit the program.

Edit menu
To perform one of the 'edit' operations without opening the menu, hold down the control key (Ctrl) and hit the function's keyboard letter For example, Ctrl-'t' (hit 't' while Control key is pressed) will make a triangle from three selected vertices.

• make Triangle (Ctrl-'t')
  When exactly three vertices are highlighted (selected and green), make Triangle becomes enabled. Hitting make Triangle creates a triangle from the three vertices (that is, if they are not already the corners of a mesh triangle). The triangle icon on the main screen shows an "incomplete" triangle when exactly three vertices are selected and they do not already make a triangle
• delete trianGle (Ctrl-'g')
  When exactly three vertices are highlighted which do make up a triangle, delete trianGle is enabled. delete trianGle only removes a triangle, not the vertices at the triangle's corners. The triangle icon shows a "shaded" triangle when Triangles thinks the three vertices actually do make a triangle
• copy selected (Ctrl-'c') copies selection to a 'clipboard', ready to be pasted.
• paste copy (Ctrl-'v') puts a copied selection (copy selected) into the mesh. The wire-frame mouse mode automatically becomes "move selected".
• duP selected (Ctrl-'p') creates an exact duplicate of the selected vertices, with whatever triangles are completely defined by the selected vertices (equivalent to 'copy' followed by 'paste'). Since the duplicate is exact, it appears 'invisible' since it is in the same place as original. However, the 'selection' is shifted to the duplicates. Use 'move selected' or 'rotate selected' under the mouse menus to move the duplicate into a visible location. (The duplicate is not connected to the original.)
• detach selected (Ctrl-'b') 'Detaches' the selection from the rest of the mesh. If the selection is connected (or consists of connected parts), this will create new connected components. For example, if a mesh has a leg connected through edges to the rest of the mesh and the leg is then 'detached', the leg will not be connected to the rest of the mesh anymore. The wire-frame mouse mode automatically becomes "move selected".
• Reflect selected (Ctrl-'r') reflects the selected vertices through the plane normal to the coordinate you choose from the popup menu. That is, Reflect X multiplies each selected vertex's x coordinate by -1.
• Delete selected (Ctrl-'d' or Del) deletes the selected vertices, and any triangles containing any of those vertices. The mouse mode automatically changes to "move selected"
• Meld vertices (Ctrl-'r') will "meld" all selected vertices into one. That vertex will be located at the 'center of gravity' of the original selection. This is a way to reduce the size of your mesh 'manually'.
• eXtrude selection (Ctrl-'x') makes a copy of the selection, and tries to connect it up to the original selection along whatever part of the mesh's boundary which is in the selection. If the selection doesn't actually contain any of the mesh's boundary, the 'extrusion' is aborted. Otherwise, the mouse mode automatically changes to "move selected"
• mArk selected (Ctrl-'a') (unmarK selected (Ctrl-'k')) "marks" ("unmarks") the currently selected vertices. What "marking" means is not stable at this point. Currently, it holds the marked vertices in place during smootH subdivision, but the way this is accomplished in the program is not quite adequate.
• Select all (Ctrl-'s') (Unselect all (Ctrl-'u')) causes all vertices in the mesh to become selected (unselected).
• snap (Ctrl-'y')
  'Snap to grid'. Pushes each vertex (or each selected vertex) onto the nearest "grid" intersection. A box appears where you choose the grid resolution, and which coordinates (x, and/or y, and/or z) to force onto the grid.
• Invert selection (Ctrl-'i') causes all unselected vertices to become selected and removes all selected vertices from the selection.
• remove 'loose' vertices
  Some operations (delete trianGle, remove selected triangles, etc) may leave unconnected vertices laying about. If you don't want them, use remove 'loose' vertices to find and delete them.
• meld coincident vertices (Ctrl-'w')
  looks for pairs of vertices within 'epsilon' distance (which you can set when invoking the 'meld coincident vertices' command) of each other and melds them into one, if they are not both vertices of the same triangle. If 'selected' is checked, looks for and melds vertices within 'epsilon' distance of the selected vertices.
• try Orient (Ctrl-'o') tries to make the mesh consistently oriented, meaning it tries to orient all normals to point "out" of the mesh, or all point "in", but this is not always possible.
• Evert selection (Ctrl-'e') reverses the "normal orientation" of triangles contained in the selection. Note that the results of this operation are usually lost during "try Orient", "smootH subdivision", and other operations which apply 'try Orient'. The orientation of triangles is not normally visible in Triangles but hitting the 'f' key will show "inward" pointing triangles as darker than "outward" oriented neighbors.
• Smooth/Divide/Reduce/Deform (Ctrl-'d') Divide, smooth, and reduce can each be applied either to the entire mesh, or to an (entire) connected component of the mesh. (A 'connected component' is a set of vertices all connected one to another by some sequence of triangle edges). To apply to a connected component, select that component ('t' followed by clicking on one its vertices), then use 'divide selection', 'smooth subdivide selection', or 'reduce selection'. If, instead of selecting a whole component first, less than an entire connected component is selected, these functions go ahead and 'do' the whole component, but if the selected vertices happen to belong to more than one component, they will pick just one of the components.
  • divide (Ctrl-'f') turns each edge of the mesh (or connected component) into two edges, connecting the vertices so that each triangle is split into 4. Note that Triangles has a limit on the number of triangles, vertices, and edges that are allowed. (currently there is a 50000 vertex, 50000 triangle, 100000 edge limit.)
  • smootH subdivision (Ctrl-'h') is basically an adaptation of John VanSickle's POV macro. It divides each triangle into 4 and tries to make the resulting mesh smooth using an algorithm invented by Charles Loop. The best results are with closed surfaces (no boundary). Outer boundaries actually sometimes become more jagged. A work around for the bad behavior of this algorithm on boundaries is: 1) before smoothing, select the mesh (or just the boundary of concern) and 'extrude' it (hit Ctrl-'x'), but don't actually move the 'extrusion'. 2) Next, remove all the new ('extruded') triangles by hitting Ctrl-'j'. 3) Remove vertices left over by the last step with 'remove loose vertices' (hit Ctrl-'l'), 4) Then go ahead and smooth (Ctrl-'h'). Finally, you can delete the 'extrusion' (hit Del). Eventually I may fix this (or at least automate this sequence of operations) but for now this seems to work pretty well. Set the smoothing scale under the 'Options' menu. Also under Smooth Subdivision options is the cryptic 'Average between marked'. Marked vertices do not move during the subdivisions. Choose 'Average between marked' (checked) to have the newly inserted edges go straight between the marked vertices. Note that the new vertices in between marked vertices are not automatically marked, and will have to be marked 'manually' between subdivision iterations in order for 'Average between marked' to work the way it sounds.
    
  • mesh ReductioN (Ctrl-'n')
    Tries to reduce the number of vertices (and hence number of triangles) by collapsing the 'least important' edges. Works best with closed (no boundary) meshes. The 'Fraction' is the fraction of the original number of mesh vertices that will be removed; e.g. a fraction of .1 will remove 10% of the vertices, leaving 90%. For each vertex to be removed, the entire calculation of 'least important edge' is done/redone, so, on larger meshes, this can take an extremely long time. Hit <ESC> key once to abort.
  • deformations
    Various ways to deform a mesh. Can be applied to either the entire mesh or a selection.
    • repulsive point
      X_new=X + c * (X-P)*e^{-a*(||X-P||^b)}
      where P is the 'repulsive point'. Pushes points of the mesh away from (c>0) or towards (c<0) the 'repulsive point'. Mesh vertices closer to the repulse point are pushed/pulled harder
      .
    • Roughen (Adapted from John Van Sickle's POV macro) displaces vertices a random amount normal to the mesh surface, making surfaces rougher. Experiment with the sequence 'diVide', 'roughen', 'diVide', 'roughen' on a mesh.
    These four are adaptations of Chris Colefax POV-Ray macros:
    • Wave
    Moves vertices as a 'wave' symmetric about the y-axis.
    • Ripple
    • Twist Twist the mesh about the specified twist center. Vertices further from the twist center are rotated more. The specified 'angle' is the rate at which the amount of rotation increases as distance of a vertex from the 'twist center' increases. With 'about Axis' checked, the twist is about the specified axis vector based at the twist center, helix-like.
    • Bend
  • delete all
    Deletes all. Start anew.

  Options menu

  • scale Uniformly. Checked, wire-frame view mouse scaling operations scale equally in the x, y, and z directions. Unchecked, the mouse scales only in the two view directions of the wire-frame view plane where you start dragging the mouse.
  • rotate about view center. When this is checked, the 'Rotate selected' mouse mode rotates the selected vertices about (0,0,0). Unchecked, the selection is rotated about the 'center of gravity' of the selection.
  • Pull fall-off rate adjusts how strongly pulling vertices with the mouse affects vertices distant from the dragged vertex. (Higher values here decrease the effect). Max Edges is a distance (in edges) separating the pulled vertex from distant vertices. When 'pulling' with Pull Edges, vertices further than Max Edges from the vertex you are pulling will not move.
  • Show 3d Axes toggles drawing the axes in the 3d view.
  • Display Resolution is for changing video resolution. Your system may not support all offered resolutions. Mine doesn't, and the 1200x1024 and 1600x1200 are untested. Please send me a note (dsharp@interport.net) to tell me your results if your system supports them to let me know how well they work.
  • Shading Palette presents a menu of base colors for the '3-d' view shading. The default grey palette is larger (more shades) than green or red.
  Polygon button:
  Opens a drawing area for drawing a polygon to be triangulated or lathed. Left-clicking the mouse creates a new polygon vertex, connected to the last-created vertex. Holding down a shift key while left-clicking forces the new vertex to be aligned horizontally or vertically with the last created vertex (whether it is aligned horizontally or vertically depends on which difference is less). A right-mouse click closes/finishes the polygon (if it has at least three vertices). Make holes in the polygon by drawing more polygons inside the first. The first shape you draw must be the 'outer' polygon and all subsequent shapes (holes) must be inside the outer shape, and no line segments are allowed to cross. Also, each polygon must be completed (closed with a right-mouse click) before the next shape is started, and a polygon will not close if the closing edge would cross any other segment. These conditions are enforced by Triangles, so if you find that the program will not place a new vertex, check for violations of these conditions. It is currently possible to draw a new 'inner' polygon around an already drawn inner polygon, but the triangulation results are unpredictable and for all I know may even cause a crash.
  
  • Triangulate triangulates the polygon and adds the polygon to your mesh. (The outer polygon and holes must be closed).
  • Lathe creates a "surface of rotation" by rotating the polygon about the y-axis. (The polygon need not be closed. But realize that you can't draw inner polygons unless the outer one is closed).
  • Pipe extrudes the polygon without filling it in (the 'pipe' is open-ended). It doesn't actually move the extruding end, so that the polygon appears to be a flat polygon, but dragging the mouse in a flat-wire-frame view will make the extrusion appear.
  The polygon drawing area may be larger than the wire-frame view areas, and larger polygons may not completely fit in the wire-frame windows when done. If the 'reScale output' check-box is checked, the polygon or lathe will be rescaled so that the edges of the polygon drawing area coincide with the edges of the XY plane wire-frame view (that is, what you draw in the polygon drawing area will fit in the wire-frame view).