Q:

How to find evenly distributed points on a line?

This is to find evenly-distributed points lying on a specific line (from a starting position, 2 points on the line, and an angle against the horizontal) and then past the second point, to draw something so it's moving at a fixed rate in a given direction.
I'm thinking about calculating a slope, which would give me vertical movement to horizontal movement. However, I don't even know how to assure they'd be the same speed in two different lines. For example, if there are two different pairs of points, how it would take the same amount of time for the drawing to travel the same distance on both.
Is what I'm describing the correct idea? Are there any methods in OpenGL that could help me?

A:

You should use vectors. Start with a point and travel in the direction of a vector. For example:
typedef struct vec2 {
    float x;
    float y;
} vec2;

That defines a basic 2D vector type. (This will work in 3D, just add a z coord.)
To move a fixed distance in a given direction, simply take some starting point and add the direction vector scaled by a scalar amount. Like this:
typedef struct point2D {
    float x;
    float y;
} point2D; //Notice any similarities here?

point2D somePoint = { someX, someY };
vec2 someDirection = { someDirectionX, someDirectionY };
float someScale = 5.0;
point2D newPoint;

newPoint.x = somePoint.x + someScale * someDirection.x;
newPoint.y = somePoint.y + someScale * someDirection.y;

The newPoint will be 5 units in the direction of someDirection. Note that you'll probably want to normalize someDirection before using it in this manner, so it's length is 1.0:
void normalize (vec2* vec)
{
    float mag = sqrt(vec->x * vec->x + vec->y * vec->y);
    // TODO: Deal with mag being 0
    vec->x /= mag;
    vec->y /= mag;
}

