CODEWITHSUNDEEP
bsp-tree
Byrd
Byrd

Reputation: 37

How can the equation for a line in 2d space be represented as an array of three values?

I am trying to understand the following function from theparticle Supposedly, the function determines the equation of a line which is represented as an array of the coordinates for two points that lie on the line: [x1, y1, x2, y2]. The function that returns the equation is:

float [ ] getLineEquation( int [ ] line) {
    float [ ] equation = new float [3];
    int dx = line[2] - line[0];
    int dy = line[3] - line[1];
    equation[0] = -dy;
    equation[1] = dx;
    equation[2] = dy*line[0] - dx*line[1];
    return equation;
}

I don’t understand how the 3-element array that is returned by this function corresponds to the equation of a line. I appreciate any help that will let me understand what this function is doing.

Upvotes: 3

Views: 62

Answers (1)

Developer
Developer

Reputation: 483

A line in 2D space can be described by y = ax + b or cx + dy + e = 0. If you take the second form of the same equation than you can represent it as [c, d, e] which is your array of three elements. I hope I understood well your question.

Upvotes: 2

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