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3D Imaging
Virtual Worlds The Spatio-Temporal Environment | Creating 3D Content The virtual world is a mathematical simulation of space and time. This virtual stage is populated with mathematical simulations of physical objects and the forces that act upon them. The laws of nature in the virtual world can mimic those of our own 'real world' or adopt the alternate characteristics of any imaginable 'possible world'. For instance, the force of gravity may be either precisely represented or completely absent as desired -- elephants can fly! 3D modeling and animation systems were developed to make this universe of possibility manageable. Conventions adopted by 3D modeling software generally describe a spatio-temporal environment and the tools and building blocks necessary to create what is intended. A brief tour of these conventions is offered through the links above. The Spatio-Temporal Environment The spatio-temporal environment is comprised of a world space in three axial dimensions; length, height, and depth (x, y, z) and a fourth dimension time. This virtual time can be expressed in terms of a sequence of image frames organized into a predetermined number of frames per second. World space is based on the mathematical three axis coordinate system developed by 17th century french philosopher Rene Descartes. Descartes recounted that the idea for the coordinate system came to him when he was a young soldier in the French army, stationed in the Netherlands, fighting the Spanish. Laying on his bed in his quarters, Descartes watched a fly buzzing around his room. As he followed the fly's movements with his eyes, Descartes wondered how he could mathematically describe the fly's path. He invented the cartesian coordinate system to chart the fly. Here's how it works. Each of the three spatial dimensions, width, height, and depth are represent by a linear axis extending infinitely in both directions. The three axes are named X for width, Y for height, and Z for depth. The three axes, (X,Y,Z), are aligned such that they all emerge from the same location, a point called the Origin. Numerical values progress evenly in both positive and negative direction along each axis. The value of zero placed at the Origin. This scheme enables every location in 3D space surrounding the Origin to be given a unique three 3D position expressed in terms of the numbers corresponding to the point's location along the X, Y, and Z axes. This 3D point location is called an (X,Y,Z) triplet. The (X,Y,Z) triplet for the Origin is (0,0,0)  Adding the fourth dimension, time, the fly's path can be described by a sequence of (X,Y,Z) triplets measured at temporal intervals along the fly's route. If a curve was drawn through the points, the curve's path would match the fly's path. If a person built a virtual fly and took a series of virtual photographs as the fly traveled along the curve, these photographs could produce an animation or interactive experience that is the full realization of Rene Descartes' invention. Cartesian space can be outfitted with encapsulating visual environments of various forms. Planar and cylindrical 'backdrops' can provide visual backgrounds. Cubic and spherical environments are able to encompass the entire virtual world. Encompassing environments mapped with High Dynamic Range (HDR) panoramic images contain sufficient information to accurately illuminate the content of a virtual world exactly as it would have appeared if it existed in the location where the panoramic HDR image was captured. Creating 3D Content 3D modeling and animation software provides many tools and methods to build 3D content. Geometry building tools enable the creation of almost any selected shape. Simple forms can be constructed by combining and modifying geometric primitives such as cubes, spheres, cones, cylinders, planes, and toruses (donuts). More complex forms are generated through the use of curves and single or multiple straight line segments combined into surface generating frameworks. Profile curves can be rotated around a central point to create revolved forms. Profile curves can be extruded along a path curve. Surfaces can be skinned across a series of 'rib' curves as in the construction of a boat hull or an airplane wing. Multiple curves can be tied together and surfaced to describe the boundaries and internal characteristics of complex organic shapes. Shapes can be pushed, pulled, attached, detached, trimmed, merged, beveled, filleted, mirrored, duplicated, sculpted, deformed, exploded, smoothed, moved, rotated, scaled and subjected to a host of other transformations. Material creation tools determine the surface attributes such as color, reflectivity, bumpiness, and transparency. Surfaces can be assigned colors and material characteristics like transparency, painted in 3D, have 2D images mapped to them, or receive an algorithmic procedural texture simulating, wood, stone, water, or many other substances. When 2D images are projected on geometry, an addressing system is laid down on the geometry's surface that assigns each pixel in the 2D image to a specific location on the surface. This operation essentially applies a two axis coordinate system corresponding to the 2D digital image to the surface of the geometry. This two axis coordinate system, is comprised of a horizontal axis 'U' and the vertical axis 'V'. Ordered pairs of UV coordinates, (U, V,), assigned to a geometry's surface are the instructions for mapping the 2D image's pixels onto the geometry.
The application of 2D image information to 3D geometry is called texture mapping. Color maps specify the colors of the surface. Bump maps simulate surface textural elements without altering the underlying geometry. Transparency maps govern surface opacity. Displacement maps generate relief by altering the actual surface geometry. All these maps are applied using UV coordinates. |
 The Origin of a 3D Cartesian Coordinate System. |
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