Math Primer: Trigonometry 101 - Flash 3D: Animation, Interactivity, and Games - page 160

Figure 5.35 shows circles on several horizontal
planes in perspective. In one-point perspective
along the z-axis, ellipses as perspectives of
horizontal circles can vary in proportion from
a straight line to nearly full circles.

The different ellipses provide a comparison
of circles of equal size that are at the same
viewing distance from the picture plane but
vary in the distances above and below the
horizon. The circles are horizontally centered
at the center of vision (COV). The plane that
is through the horizon generates a straight line
edge of the circle.

Horizon

COV

When we move from simulated 3D to actual
3D using one-point perspective along the z-axis,
it will be quite easy to look at objects rotating in
different horizontal planes relative to the horizon.
We'll see what's involved in the next chapter.

Figure 5.35 Circles on horizontal
planes in perspective

Summary

This chapter focused on trigonometry. Key concepts to remember include the following:

• Flash measures angles in radians.

• The Pythagorean theorem states that for a right triangle, the square
of the hypotenuse is equal to the sum of the squares of the other
two sides.

• Sine, cosine, and tangent represent the three ratios of the sides of a
right triangle in relation to the angles of the triangle.

• The trig functions are useful for creating circular and elliptical motion.

• The atan2 function is useful when you have two points and want to
know what angle they make with each other.

The next chapter focuses on the fundamentals of 3D space.