Ruled Surfaces

In Conclusion

If the material in this chapter was not review for you, please experiment with some of the functions. Use the circle drawings to plot out several curves. Also, read Appendix A to get an explanation of how to compute the derivative of trigonometric functions. These functions are not used too often in the rest of the chapters, but I thought there were several concepts that were worth talking about. Trigonometry is extremely useful for dealing with angles and you will work with angles frequently in game development. Before moving on to the new material, let me enumerate some of the more important points from this chapter.

• Trigonometry is used to describe the relationship between the angle of a line and the x and y distances it covers.

• Sine, cosine, and tangent are the three most frequently used functions. They describe the ratios of the sides of triangles as a function of an angle.

• All three functions are periodic.

• The exact shape of a wave is determined by its amplitude, wavelength, and phase.

• The frequency of a wave is the inverse of its wavelength.

• Trigonometric functions can be approximated with Taylor series representations.