3D Graphics Pipeline

Transcription

1 3D Graphics Pipeline The common denominator to all 3D Graphics: The Pipeline Regardless of the 3d graphics application, whether it is animated motion pictures, video games, CAD (computer aided design) programs used in mechanical engineering or architecture, virtual reality, cell phones or simulators, the 3d graphics pipeline is the common element to all of these. The 3D graphics pipeline consists of these blocks of software: Object Transformations Camera Transformation Back-face Culling Clipping Perspective View Objects, Camera(s) and Lights have Transformations. A Transformation rotates, scales and moves (translation) an object in 3D space. For example, the Earth has three transformations operating on it : one for the Earth's annual rotation around the Sun; another for the annual tilt of Earth's seasons; And finally the Earth's daily rotation around it's axis. Then there is the camera's point-of-view. The point-of-view could be from the Sun, a satellite over the equator, or a camera from the International Space Station. 3D Mesh, Coordinates and Coordinate Indexes Figure 1: Wireframe of Teapot Figure 2: Teapot Rendered Each 3D object is made up of a mesh similar to the chicken-wire mesh that forms the shape of a New Year's Day Rose Parade float. The points of this mesh, known as vertices, are made up of three values: x, y, z. In Figure 1, the wireframe shows the vertices wherever two or more white lines meet. These vertices or points are organized in a list known as a coordinate Index. For example, the simplest 3d object is the polygon and while the teapot shows many polygons of four vertices, most as made up of three vertices. Each polygon is required to have its vertices planar, meaning they exist in a single plane. Think of a chair with three legs it won't

2 wobble because all the legs will be flat on the floor, with the floor acting as our plane. However, if we have a four-legged chair, it may wobble or tip because not all the legs are touching the floor, and thus the bottom of those 4 legs, which could represent the four points of our polygon, are not planar. The simplest 3D object is a line just a beginning and ending vertex But lines only make meshes. Polygons can be filled in to create an object like the rendered teapot in figure 2. Each polygon is made up of at least 3 connected vertices. We specify the vertices as a set of three values which are x, y and z. We will use the X3D file format to be discussed later. <Coordinate point=" "/> The first vertex is 1.0, 2.0, -1.0; the second is -2.0, -3.0, -2.5; the third vertex is 3.0, -0.5, 0.0. These vertices are connected by a coordinate index specified inside a shape node as such: <Shape> <IndexedFaceSet coordindex=" "> <Coordinate point=" "/> </IndexedFaceSet> <Appearance><Material/></Appearance> </Shape> This is how the X3D file format would specify a shape. Each shape node consists of geometry and an appearance. The X3D file format specifies objects, lights, cameras and animations in a 3d scene. It is based on XML, the extended Markup Language, a International Standard for specifying data from bank accounts to news information. The geometry contained in the above Shape object is an IndexedFaceSet, which contains a Coordinate list that specifies a set of points (vertices). Other geometry includes a PointSet which is just a set of dots, an IndexedLineSet which is a set of connected lines, and finally some built-in primitives which are: Box, Cone, Cylinder, and Sphere. The IndexedFaceSet contains a 'coordindex' which lists which points are connected to create polygons. In the above example, coordinate 0, 1 and 2 are connected. The '-1' ends the list of connected points for this polygon. Remember that a polygon can have three or more vertices so we need '-1' to indicate this is the last vertex of this polygon. Later, we will describe 3d meshes made up of multiple polygons just like the teapot above. Note that the order of the polygons are counter-clockwise and order determines if a polygon is facing toward you, or away from you. Coordinate #0 with x, y, z postion (1.0, 2.0, -1.0) is at the top, connected to coordinate #1 on the lower left at (-2.0, -3.0, -2.5), connected to coordinate #2 on the far right at (3.0, -0.5, 0.0). Transforming Coordinates In the 3D Graphics Pipeline, each coordinate is multiplied by a stream of matrices to move (translate), rotate and scale the objects. There may be multiple transformations on an object. A person's hand has a rotation at

3 the wrist, elbow, shoulder and even the persons body. Each one of these rotations is a transformational matrix. It might be worth reviewing matrix multiplication, but here is a simple example that each X, Y, Z coordinate will be multiplied by a matrix. [Transformation =[Transformed Coordinate [ m 11 m 12 m 13 m 14 X Xm11 + Ym12 + Zm13 + m14 m 21 m 22 m 23 m 24 Y Xm21 + Ym22 + Zm23 + m24 m 31 m 32 m 33 m 34 Z Xm31 + Ym32 + Zm33 + m Transformation Matrices Without any transformations, all object would be located at the origin of our 3d world. Those objects include the actual 3d meshes and lights. 3D meshes may also include child objects, which are 3d meshes but attached to the parent object. For an animated character, the mesh of a hand is a child object of an arm. Whereever the arm goes, the hand goes with it. Another example is the Moon being a child of the Earth. As the Earth goes in its annual rotation around the Sun, the Moon follows along. There are five 4x4 matrices related to object transformations: translation (movement), scale and a rotation matrix around each object. [ Translation Tx Ty Tz [ Scale Sx Sy Sz 0 [ X-axis cos ϴ -sin ϴ 0 0 sin ϴ cos ϴ 0 [ Y-axis cos ϴ 0 sin ϴ sin ϴ 0 cos ϴ 0 Note that the lines are added inside the matrices to more clearly show the columns

4 [ Z-axis cos ϴ -sin ϴ 0 0 sin ϴ cos ϴ Each of these five 4x4 matrices multiplies each vertex of a 3d mesh. But as we shall see in later lectures, there will be more efficient ways to perform this multiplication. Camera Transformation The Camera Transformation transforms all the objects such that the camera is at the origin. This involves rotating all the axis such that the camera is now the new origin. For an artist using a 3d modeling program, they simply set the location of the camera and the target where the camera is focused, but the math for the camera transformation is far more complex and will be covered in a future lecture. Back-face Culling Once all the objects are in place including the camera, it is time to get rid of polygons that can't be seen. No point in wasting computing power with polygons that can't be viewed by the camera. This is known as 'backface culling' and effectively removes all the polygons which are not visible to the camera. It's much like looking at one's hand you can either view the front of your hand, or the back of your hand, but not both (barring the use of a mirror). Back-face culling removes polygons at an angle greater than 90 degrees from the camera Clipping Clipping removes additional polygons that are outside our field-of-view - objects that are behind us, too far right, left, above or below us. In addition, we also clip objects too far away which likely would be too small to draw or be noticeable. Additionally, we also clip objects too close. If the object gets right in front of our camera, it blocks our view of anything else and thus, must be clipped. Clipping also 'slices' a polygon where part of it is viewable and the other part is not. The polygons crosses the edge of our 'view frustum'. The View Frustum is a four sided pyramid with the top being our camera and the base being the far clipping plane. The View Frustum is also based on our field-of-view. Perspective View At the end of the 3D graphics pipeline, is perspective view, another 4x4 matrix that makes objects in the distance much smaller, just as we see the world. The perspective view matrix also 'collapses' the world onto a 2d plane. Effectively, the z-value of every vertex will be the same. That allows us to drop the z-value from each (x, y, z) vertex leaving just the X and Y values, much like a 2D image. Then a simple calculation coverts the origin from the center of the world, to screen coordinates where (0, 0) is located in the upper left side. Summary

5 This list of transformations object transformation; camera transformation; back-face culling and clipping to remove unseen polygons and finally perspective view make-up the 3D graphics pipeline. Once concluded, we can calculate the lighting and apply the materials to the visible objects.