cross and dot product

General Discussion Other

clankill3r

in General Discussion • Other • 1 year ago

I want to understand the dot and cross product of a vector.

However as often i don't understand the wikipedia and looking at the code of PVector isn't really helpfull either.

If someone could explain to me (with a example prefered) what it is and what it's good for then that would be really nice.

Replies(3)

kooogy

cross product will give you a vector mutually perpendicular to the two vectors used as input. useful for calculating the normal of a polygon, for use in lighting. and for backface culling.

dot product gives you the projection of one vector onto another. um, hard to explain. can be used to find the angle between them.

khan academy video: http://www.khanacademy.org/science/physics/v/cross-product-1

interactive examples:
http://mathinsight.org/dot_product
http://mathinsight.org/cross_product

clankill3r

Re: cross and dot product

1 year ago

I think i'm starting to understand a little.

Only worked on the cross product so far, it's not easy.

I hope daniel shiffman finish his upcoming book soon.

import processing.opengl.*;
PVector a, b;
void setup() {
size(400, 400, OPENGL);
a = new PVector(0, 100);
b = new PVector(100, 50);
}
void draw() {
background(0);
translate(width/2, height/2);
rotateX(map(mouseY, 0, height, 0, TWO_PI));
rotateY(map(mouseX, 0, width, 0, TWO_PI));
stroke(0, 0, 255);
line(a.x, a.y, a.x, 0, 0, 0);
stroke(0, 255, 0);
line(b.x, b.y, b.z, 0, 0, 0);
noStroke();
fill(255, 80);
triangle(a.x, a.y, 0, 0, b.x, b.y);
PVector c = a.cross(b);
stroke(255, 0, 0);
line(c.x, c.y, c.z, 0, 0, 0);
}

allonestr..

Re: cross and dot product

1 year ago

As kooogy said the cross product is mutually perpendicular to two existing vectors. Think of a pen perpendicular to a sheet of paper (the plane of the paper is defined by two non-colinear vectors).

Another way of thinking of the dot product is that it's the shadow of one vector onto a second vector. Imagine a ladder leaning against a wall. The dot product of the ladder and the ground (ladder dot ground) is the distance from the foot of the ladder to the wall; and the dot product of the ladder and the wall (ladder dot wall) is the distance from the top of the ladder to the ground.