General 3D Modeling Terms

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General 3D Modeling Terms

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General 3D Modeling Terms

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This chapter covers the common 3D modeling term definitions:
- coordinate system
- generic units
- Vertices, Pivot Point, Edges and Faces
- UV texture mapping
- mesh versus FFD

Please make yourself familiar with these terms. They will be used in the following chapters when the Warper interface and workflow is being explained. As well, the explanations might help you when communicating with 3D artists who prepare 3D models for you or when getting in touch with one of the third party applications yourself.

Coordinate System

Each 2D and 3D world needs a coordinate system which defines the position and orientation of each object. There are two possible systems: the right-handed and left-handed system. In both systems the positive X and Y direction are the same and show to the right and upper side (as seen in the picture below). The Z axis makes the difference, it shows either to the back or to the front.

Pandoras Box and the Warper are based on the left-handed system. If you import an object from an application that is based on another orientation make sure to adapt it.

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The origin of the 3D space (X,Y,Z) = (0,0,0) is situated in the exact middle of the screen when starting Pandoras Box and the Warper with default settings. The origin is the reference point for every object. The camera has a position of (0,0,-25) and a FOV (field of view = opening angle) of 35,489 degree (or 56,251 mm).

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Generic Units

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Next to the coordinate system's orientation, units are of great importance. An object has a defined position and size which is defined and saved in units.

Many 3D modeling programs can save an object with so called generic units (GU), e.g. a cube may have a height/width/depth of 8 GUs, rather than being measured in metric or pixel units. The advantage is that GUs adapt to the current screen, they "generate" a relative size and must not be scaled when the resolution changes. Per default a screen width is exactly 16 GUs, the height is calculated by the aspect ratio. Hence, a 4:3 display is 16 GUs wide and 12 GUs high, whereas a 16:9 display has the same width but a height of 9 GUs.
For example: A 3D modeler works an a 1024x768 pixel display and creates a cube that covers half of his display, i.e. it is 8GUs wide. If you import the cube into the Warper it will have the same relative size (half of your display) no matter which aspect ratio or resolution is chosen at your computer.
The height will always be the same size as the width, it will never be "squeezed", however it might cover less or more space than on the modelers screen.

The Warper and Pandoras Box are based on generic units since version 5. The coordinates (X,Y) = (0,0) are situated in the middle of the display. If a layer or object moves 8 units to the right its center will be exactly on the right edge of the screen.

Vertices, Pivot Point, Edges and Faces

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Every 3D model and geometric shape consists of corners and intersections. These special points are saved as so called "vertices" (singular: "vertex"). In a 3D space a vertex must consist of three coordinates, X,Y and Z to definitely mark the position of a corner. A cube, for example must be defined by a minimum of 8 vertices. In the example, these are the small blue points.

The default mesh in the Warper consists of vertices as well, the more mesh segments you set up, the more vertices are generated by the Warper.

In most 3D modeling programs there is a so called pivot point. In the left image it is depicted as a round orange point. The pivot starting point is the center of a transformation like rotation and scaling. If the cube is scaled, all vertices still would have the same distance to the pivot point. For more examples, please see the topics Scale Pivot and Rotation Pivot in Pandoras Box.
In the 3D modeling program itself you may position the pivot point where you like but please keep in mind that file formats like *.x, *.fbx and *.3ds do not support pivot points. These formats always save the coordinates of the vertices as absolute coordinates. That means that the position of the object and all its vertices will be kept. But when importing the object in the Warper, the center of rotation and scaling is the center of the object itself. This cannot be influenced. Pandoras Box, on the other hand, supports pivot points itself. Thus, when importing the object, the pivot point is set to the origin of the coordinate system (0,0,0) and can be moved to the position of your choice with the parameters of the layer.

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The connections between two vertices are called "edges". Here, they are depicted as orange lines. A cube consists of 12 edges.

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Some 3D modeling programs define that exactly three vertices make one face. Thus faces are always triangular.

The next hierarchy is then called "polygon" whereas one or more face(s) form one polygon. The outlines from a polygon are the edges.
In the example image they are 6 gray squares forming a cube; 6 polygons. If faces exist, there would be at least two faces per polygon.

 

No matter how your 3D modeling program works, either faces or polygons can be applied with a texture.

UV Texture Mapping

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UV mapping is a process of defining how to represent a 2D image on a 3D model.
The UV mapping transforms a 2D source image (in our case an image or video) into an image buffer called a texture.
In contrast to "X", "Y" and "Z", which are the coordinates for the rendered 3D object, "U" and "V" are the coordinates of the texture. The UV map stores for each X,Y,Z- coordinate a defined U,V-coordinate.

This creates the effect of painting the image onto the surface of the 3D object, or in other words, how to wrap or stretch the image around the object. As explained below there are different ways how to do that, hence the chosen UV map is stored as a property of the 3D model.

If a 3D model has no UV map, neither the Warper nor Pandoras Box can paint a texture on it which leads to the fact that the object is invisible and cannot be displayed. The Warper has tools that can influence the UV Map, e.g. scale or move it. When not importing 3D models from third party programs but working with meshes in the Warper you can define how to apply a texture on it. A texture can cover more than one mesh as well. This is described in the chapter "Edit Menu".
On the Pandoras Box side, there are effects influencing the UV map as well.



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There are several standard mapping techniques available to map a texture onto an object:
- planar
- cubic or box
- cylindrical and
- spherical mapping.

Planar mapping can be referred to an image projection from one side onto an object.

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A cubic mapping for example maps the texture to all sides of a object like a box.

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The cylindrical mapping wraps an image around an object like a cylinder, the left and right edge will join each other.

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Spherical mapping wraps the image all around an object as a sphere. Please be aware that the top edge of the texture shrinks down into the top north pole and the bottom edge in the south pole.

For proper spherical mapping textures with an aspect ratio of 2:1 apply best to a spherical object.

Mesh versus FFD

This paragraph describes the difference between a mesh point and an FFD point, thus it is covering a fundamental function of the Warper.
The pictures below show a 2D plane with a green-colored 10x10 mesh and orange-colored 3x3 FFD.

See here the differences between moving a FFD control point and moving a mesh point. Please note that the FFD is only a helping tool to set up the mesh, you won´t see the FFD in the exported object.

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a. The grid without any editing. The green lines represent the mesh, the orange lines the FFD.

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b. The top left FFD control point is moved further down. The whole mesh is affected by this change: the horizontal lines are bend together on the top left side, the meshes outline gets curved.
This effect can be of advantage or disadvantage. In the beginning of the warping process it can simplify and accelerate the workflow as it is not necessary to move each individual mesh point. The further the warping process develops the more it is necessary to apply changes to particular pixels only. At this point the FFD is not sufficient any more as it affects large areas of the grid.

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c. One mesh point is moved. Only the segment lines between the moved point and the four neighbor mesh points are affected by this.
The more you are experienced with warping the better you will be able to answer the question how many mesh points a grid should have. If too little points are chosen it won't be possible to apply the detail changes that are necessary. This is especially crucial when setting up meshes for a softedge projection as the pixels must overlap each other exactly in the overlapping area.
If too many points are chosen, the warping process is lengthened unnecessarily as all points must be adjusted.

For more information about how to use the Warper please refer to the following pages:
User Interface,
Warping Guide,
Keyboard Shortcuts

If you are interested in other 3D modeling programs, please refer to the topic covering third party applications.