By Fletcher Dunn
This attractive booklet provides the basic arithmetic had to describe, simulate, and render a 3D international. Reflecting either educational and in-the-trenches useful event, the authors train you ways to explain items and their positions, orientations, and trajectories in 3D utilizing arithmetic. The textual content presents an advent to arithmetic for video game designers, together with the basics of coordinate areas, vectors, and matrices. It additionally covers orientation in 3 dimensions, calculus and dynamics, pix, and parametric curves.
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Additional info for 3D Math Primer for Graphics and Game Development, 2nd Edition
2 Specifying Locations in 3D In 3D, points are specified using three numbers, x, y, and z, which give the signed distance to the yz, xz, and xy planes, respectively. This distance is measured along a line parallel to the axis. For example, the x-value is the signed distance to the yz plane, measured along a line parallel to the x-axis. Don’t let this precise definition of how points in 3D are located confuse you. 11. 3. 2, all 2D coordinate systems are “equal” in the sense that for any two 2D coordinate spaces A and B, we can rotate coordinate space A such that +x and +y point in the same direction as they do in coordinate space B.
17. The (x, y) coordinates of the endpoint of a ray thus rotated have special properties and are so significant mathematically that they have been assigned special functions, known as the cosine and sine of the angle: Defining sine and cosine using the unit circle cos θ = x, sin θ = y. 4. Odds and Ends 23 You can easily remember which is which because they are in alphabetical order: x comes before y, and cos comes before sin. The secant, cosecant, tangent, and cotangent are also useful trig functions.
Any description of a position is meaningful only in the context of some (typically “larger”) reference frame. Theoretically, we could establish a reference frame encompassing everything in existence and select a point to be the “origin” of this space, thus defining the “absolute” coordinate space. However, even if such an absolute coordinate space were possible, it would not be practical. Luckily for us, absolute positions in 39 40 2. Vectors the universe aren’t important. Do you know your precise position in the universe right now?
3D Math Primer for Graphics and Game Development, 2nd Edition by Fletcher Dunn