Ray-Plane Intersection

0
votes

I'm having a hard time following the ray-plane intersection described in the following page.

SIGGRAPH Ray-Plane Intersection

Here is my understanding.

The plane is described as Ax + By + Cz + D = 0

or

The Vector ( A, B, C, D ), Where A, B, C define a normal plan. If A, B, and C define a unit normal, then the distance from the origin [0, 0, 0] to the plan is D.

My question is shouldn't D be a vector? Since it represents the distants between two points. I guess I just don't understand how you can represent the distance between to points as a non vector.

Any help is much appreciated.

2
raytracing
<A, B, C> describes a normal vector. That, is a vector that is orthogonal (perpendicular) to the plane. There's another way to write the formula for a plane: A(x - x0) + B(y - y0) + C(z - z0) = 0 – Joel Cornett

2 Answers

1
votes

Distance between two points is ALWAYS a scalar, a single number. Think of the vectors as points in space, right? So, when you say distance between two vectors, you are finding the distance between those two points which is a number. Distance between two vectors is the magnitude of the difference vector of the two vectors. So, you subtract the 2 vectors, get the difference vector and find its magnitude. That is your distance which is a SCALAR and NOT a vector.

0
votes

Distance is a scalar value, not a vector. It is, in fact, the length of a vector.

You can think of a vector as a set of values describing a point in space in relation to the origin. In R3, you need a minimum of 3 pieces of information to describe the location of that point. These pieces of information give you a direction and a distance.

If you were to tell me that a city is 50 miles away, that would be you describing a distance. Of course, you will not have told me which direction that city was. When you give me 2 pieces of information, you have given me a vector, as opposed to scalar value.

Also recall the formula for distance:

D = sqrt(x^2 + y^2 + z^2)

Scalar value ;)