You may remember from your high school Trigonometry class (don't worry if not, it was a long time ago for me too!) those two periodic functions, sine (pronounced "sign") and cosine ("co-sign"). They're essentially the same function and you could map one to the other with a slight shift. Cosine has some unique applications of its own, such as determining light intensity based on viewing angle, but the demos below will focus primarily on sine waves.
Notice a few interesting properties from the graph above. One is that a sine wave repeats itself every 2π (π ≈ 3.14159) or 360 degrees along the X-axis. Another is that it oscillates between the Y values -1 and 1. We write the function y = sin(x) to indicate the Y value as a function of X; see from the graph above that Y = 0 when X is any multiple of π and Y is either 1 or -1 (the peaks and valleys) when X is an odd multiple of π/2.
Point Light Demo - Download Program!
This demo shows how sine waves can be used to animate a light source. Use the specified keys to combine waves, creating a variety of unique horizontal and vertical motion paths.Before learning this elegant method, my approach to animating an object that sways back and forth, or moves repeatedly up and down along a pole, was to use code like this in my update loop:
static bool moveUp = true;
if (moveUp)
{ if (shipPos.y < 100) shipPos.y += value; else moveUp = false; }
else
{ if (shipPos.y > -100) shipPos.y -= value; else moveUp = true; }
Ocean Waves Demo - Download Program!
This demo illustrates the effects of adding sine waves and two different wave types, circular and directional. Use the specified keys to play with parameters and change the wave patterns.As with the Point Light demo, you will need to have DirectX (from Windows Update) installed in order to run the program.
These are just a couple applications of the sine function. Because of its periodic repetition, it could have many potential uses; some fellow GCG forum members cited their implementations of a 3D carousel and a wavy spaceship flight path as additional examples.
I hope you enjoy the demo programs of this post, though I admit I still need to learn better methods of input handling. Part two will describe wave alterations, based on the Ocean Waves demo, in greater detail. Until then, feel free to let us know: What's the coolest thing you've done with sine/cosine waves?
I know this image is far below par in terms of graphical work typically posted on this blog, but it's actually a very rudimentary game design I created in a matter of two minutes! Ian describes how simple it can be to create a game, and honestly anyone can do it. I call my game "Rat Race", with the concept being that two rat tokens are placed at the start and their goal is to be the first to get to the cheese. Each player must roll the die and get the numbers in order to advance (e.g. roll a 1 to advance to place "1", then roll a 2 to advance to "2", etc.) sequentially all the way from space "1" to the goal at "5". If a player rolls a "6" they send their opponent back to the start position but also forfeit their turn. They do not advance if they roll a number out of turn (e.g. roll anything other than a 1 from the start position).
