CSC418H1 Lecture : Curves
Document Summary
There are multiple ways to represent curves in two dimensions: explicit: y = f (x), given x, nd y. The explicit form of a line is y = mx + b. There is a problem with this representation what about vertical lines: implicit: f (x, y) = 0, or in vector form, f ( p) = 0. The implicit equation of a line through p0 and p1 is (x x0)(y1 y0) (y y0)(x1 x0) = 0. The direction of the line is the vector ~d = p1 p0. So a vector from p0 to any point on the line must be parallel to ~d. Equivalently, any point on the line must have direction from p0 perpendic- ular to ~d = (dy, dx) ~n. This can be checked with ~d ~d = (dx, dy) (dy, dx) = 0. The vector ~n = (y1 y0, x0 x1) is called a normal vector.
