| << Chapter < Page | Chapter >> Page > |
All of the static top-level 2D classes in the existing game-math library were renamed with a suffix of 2D to distinguish them from the new top-level 3D classes. All of the new top-level 3D class names have a 3D suffix.
The ColMatrix2D and ColMatrix3D classes
From the very beginning, the game-math library has contained a statictop-level class named ColMatrix . In the updated version of the library, that class has been renamed ColMatrix2D .
Basically, the ColMatrix2D class provides a container for a pair of values of type double with appropriate methods for accessing those values. (I explained the original ColMatrix class in detail in an earlier module.) Similarly, the new ColMatrix3D class provides a container for three values of type double with appropriate methods for accessing those values.
Objects of the ColMatrix2D class are the fundamental building blocks for several of the other 2D classes in the library, and objects of the ColMatrix3D class are the fundamental building blocks for several of the other 3D classes in the library.
Behavior of the GM01.convert3Dto2D method
The convert3Dto2D method converts a ColMatrix3D object that represents a point in 3D space into a ColMatrix2D object that represents the projection of that 3D point onto a 2D plane .
The purpose of the method is to accept x, y, and z coordinate values describing a point in 3D space and totransform those values into a pair of coordinate values suitable for being displayed in two dimensions. The math that is implemented by this methodto do the projection is described on a web page that seems to move around a bit but the last time I checked, it was located at (External Link) If you don't find it there, try (External Link) In any event, a Google search should expose numerous pages that explain the math for projections of this type.
The transform equations
I won't attempt to justify or to explain the transform equations that are used to accomplish the projection in this module. Rather, I will simplyuse them as presented in the above resource. In the meantime, if you are interested in more information on the topic, you will find a wealth of information on 3D to 2Dprojections by performing a Google search for the topic.
The transform equations along with some of the assumptions that I made in the use of the equations are shown in Listing 2 .
| Listing 2 . Transform equations for an oblique parallel projection from 3D to 2D. |
|---|
The transform equations are:
x2d = x3d + z3d * cos(theta)/tan(alpha)y2d = y3d + z3d * sin(theta)/tan(alpha);
Let alpha = 45 degrees and theta = 30 degreesThen: cos(theta) = 0.866
sin(theta) = 0.5tan(alpha) = 1;
Note that the signs in the above equations dependon the assumed directions of the angles as well as
the assumed positive directions of the axes. Thesigns used in this method assume the following:
Positive x is to the right.Positive y is up the screen.
Positive z is protruding out the front of thescreen.
The viewing position is above the x axis and to theright of the z-y plane. |
Notification Switch
Would you like to follow the 'Game 2302 - mathematical applications for game development' conversation and receive update notifications?
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|