Math 2D

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General notes:

theta_radians is an angle between 0 and 2PI.
sqr means sqaure e.g. sqr(5) = 5 * 5 = 25
sqrt means square-root, e.g. sqrt(25) = 5

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Calculate the distance between two points:

///
/// Get the distance (direct line of sight) between (x1, y1) and (x2, y2)
///
double GetDistance(const double x1, const double y1, const double x2, const double y2)
{
	const double delta_x = x2 - x1
	const double delta_y = y2 - y1;
	const double distance  = sqrt(sqr(distance) + sqr(distance))
	return distance;
}

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Rotate a point around an ellipse/circle from the center point:

const double edge_x = center_x + cos(theta_radians) * radius_width;
const double edge_y = center_y + sin(theta_radians) * radius_height;

(theta_radians is an angle between 0 and 2PI)

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Calculate the edge point of an ellipse using the angle:

const double c = cos(theta_radians);
const double s = sin(theta_radians);

const double edge_x = (radius_width * radius_height * c) / sqrt(sqr(radius_height * c) + sqr(radius_width * s));
const double edge_y = (radius_width * radius_height * s) / sqrt(sqr(radius_height * c) + sqr(radius_width * s));

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Convert a radian into a degree:

double ToDegrees(const double radians)
{
    return (radians * 180.0) / PI;
}

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Convert a degree into a radian:

double ToRadians(const double degrees)
{
    return (PI / 180.0) * degrees;
}

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Get whether a point is within a line:

///
/// Find out whether a given point (x, y) is within a line (x1, y1) -> (x2, y2)
///
bool IsWithinLine(const double x1, const double x1, const double x2, const double y2, const double x, const double y)
{
	bool within_line = false;
	
	const double delta_x = x2 - x1;
	
	if (delta_x == 0)
	{
		if (x == x1)
		{
			const double miny = min(y1, y2);
			const double maxy = max(y1, y2);

			if (y >= miny && y <= maxy)
			{
				within_line = true;
			}
		}
	}
	else
	{
		const double delta_y = y2 - y1;
		const double m = abs(delta_y) / abs(delta_x);
		const double b = y1 - (m * x1);
		
		if (y == round((m * x) + b))
		{
			within_line = true;
		}
	}

	return within_line;
}

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Get the angle of a line from the horizontal line:

///
/// Get the angle of a line (x1, y1) -> (x2, y2) against the horizontal line
///
double GetLineAngle(const double x1, const double y1, const double x2, const double y2)
{
	double theta_radians = 0;
	const double delta_x = x2 - x1;
 
	if (delta_x == 0)
	{
		if (y2 > y1)
		{
			theta_radians = 0;
		}
		else
		{
			theta_radians = PI;
		}
	}
	else
	{
		const double delta_y = y2 - y1;
		
		theta = atan(delta_y / delta_x);
		if ( p2x > p1x )
		{
			theta_radians = PI / 2.0 - theta;
		}
		else
		{
			theta_radians = PI * 1.5 - theta;
		}
	}
 
	return theta_radians;
}

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