Equation of line in the Homogeneous coordinate system

In the ordinary affine plane a straight line has an equation ax + by + c = 0. Take homogeneous coordinates and replace x by ^x/_z and y by ^y/_z and get an equation a ^x/_z + b ^y/_z + c = 0 or ax + by + cz = 0 (a homogeneous equation).

1. What is homogeneous line?
2. What is the line in homogeneous coordinates joining the inhomogeneous points?
3. What is a homogeneous coordinate system?
4. How do you find homogeneous coordinates?

What is homogeneous line?

The homogeneous co-ordinates of the line in the Euclidean plane define the plane between the two rays in the projective space. When two lines intersect in the Euclidean plane, they define a ray that passes through the intersection point in the Euclidean plane.

What is the line in homogeneous coordinates joining the inhomogeneous points?

In homogeneous coordinates the line becomes Y=0 which yields the solution (X,0,0), the ideal point associated with the horizontal direction.

What is a homogeneous coordinate system?

In mathematics, homogeneous coordinates or projective coordinates is a system of coordinates used in projective geometry, as Cartesian coordinates used in Euclidean geometry. It is a coordinate system that algebraically treats all points in the projective plane (both Euclidean and ideal) equally.

How do you find homogeneous coordinates?

Given a point (x, y) on the Euclidean plane, for any non-zero real number Z, the triple (xZ, yZ, Z) is called a set of homogeneous coordinates for the point. By this definition, multiplying the three homogeneous coordinates by a common, non-zero factor gives a new set of homogeneous coordinates for the same point.