Projecting one vector onto another... why?
Post: #16
Can you add the bit for Vperp, i dunno the formula.
Code:
// <applet code="ProjectingVectors.class" width="400" height="400"></applet>
import java.awt.Graphics;
import java.awt.Color;
import java.awt.event.*;
public class ProjectingVectors extends java.applet.Applet {
int dragMode;
int nx, ny;
int vx, vy;
int scX, scY;
Vect2D n, v;
Vect2D vParr, vPerp;
double nDv, nAbs, scale;
public void init() {
nx = (int)(Math.random()*400);
ny = (int)(Math.random()*400);
vx = (int)(Math.random()*400);
vy = (int)(Math.random()*400);
addMouseListener(new ML());
addMouseMotionListener(new MML());
}
public void paint(Graphics g) {
n = new Vect2D(nx-200, ny-200);
n.mult(1.0/200.0);
v = new Vect2D(vx-200, vy-200);
v.mult(1.0/200.0);
nDv = n.dot(v);
nAbs = n.absSqrd();
scale = nDv/nAbs;
nAbs = Math.sqrt(nAbs);
vParr = n.dup();
vParr.mult(scale);
scX = (int)(vParr.x*200+200);
scY = (int)(vParr.y*200+200);
g.setColor(Color.white);
g.fillRect(0, 0, 400, 400);
g.setColor(Color.black);
g.drawLine(200, 200, nx, ny);
g.drawLine(200, 200, vx, vy);
g.setColor(Color.red);
g.drawLine(200, 200, scX, scY);
g.drawLine(200-1, 200, scX-1, scY);
g.drawLine(200+1, 200, scX+1, scY);
g.drawLine(200, 200-1, scX, scY-1);
g.drawLine(200, 200+1, scX, scY+1);
g.setColor(Color.black);
g.fillOval(nx-2, ny-2, 4, 4);
g.fillOval(vx-3, vy-3, 6, 6);
g.drawString("N = ("+Double.toString(round(n.x))+", "+Double.toString(round(n.y))+")", nx+5, ny+5);
g.drawString("V = ("+Double.toString(round(v.x))+", "+Double.toString(round(v.y))+")", vx+5, vy+5);
g.drawString("N.V = ("+Double.toString(round(nDv))+")", 10, 20);
g.drawString("|N| = ("+Double.toString(round(nAbs))+")", 10, 40);
}
public double round(double val) {
int tmp = (int)(val*100);
return (double)tmp/100.0;
}
class ML extends MouseAdapter {
public void mousePressed(MouseEvent e) {
dragMode = 0;
if((Math.abs(e.getX()-nx) < 5) && (Math.abs(e.getY()-ny) < 5))
dragMode = 1;
else if((Math.abs(e.getX()-vx) < 5) && (Math.abs(e.getY()-vy) < 5))
dragMode = 2;
}
}
class MML extends MouseMotionAdapter {
public void mouseDragged(MouseEvent e) {
if(dragMode == 1) {
nx = e.getX();
ny = e.getY();
repaint();
}
else if(dragMode == 2) {
vx = e.getX();
vy = e.getY();
repaint();
}
}
}
}
class Vect2D {
double x, y;
public Vect2D(double x, double y) {
this.x = x;
this.y = y;
}
public Vect2D dup() {
return new Vect2D(x, y);
}
public void mult(double n) {
x *= n;
y *= n;
}
public double absSqrd() {
return x*x+y*y;
}
public double dot(Vect2D b) {
return x*b.x+y*b.y;
}
}Sir, e^iπ + 1 = 0, hence God exists; reply!
Post: #17
Thanks for the help everybody 
With everybody's explanations I'm a lttle closer to understanding why the fornula might be usefui, and I was, at last, able to figure out where I was going wrong to get such odd results (which was caused by an error in an area in no way related to the formula 
)
@unknown: if I understand you correctly: Vperpendicular = V - Vparallel
With everybody's explanations I'm a lttle closer to understanding why the fornula might be usefui, and I was, at last, able to figure out where I was going wrong to get such odd results (which was caused by an error in an area in no way related to the formula )@unknown: if I understand you correctly: Vperpendicular = V - Vparallel
Mark Bishop
Post: #18
Ok, its just mazilurik seemed to calculate it some way like this (2, 3) * ((3, 1).(2, 3))/|(2, 3)|^2 and i couldnt see (2, 3) in the diagram anywhere.
Sir, e^iπ + 1 = 0, hence God exists; reply!
Post: #19
(2, 3) is the vector perpendicular to n; I found the "component" of v perpendicular to n by finding the "component" parallel to a vector perpendicular to n. If you're already finding v-parallel, it's easier to just subtract as Sealfin said.
Post: #20
by component do you mean length
Itd be good finding the fasted way of calculating them independently because you probably wont need both.
Itd be good finding the fasted way of calculating them independently because you probably wont need both.
Sir, e^iπ + 1 = 0, hence God exists; reply!
Post: #21unknown Wrote:by component do you mean length
Yes; I used "component" (in quotes; not a technically proper usage of the term) because I like to think of projections in the same sense as the x and y components of the vector, except based on an arbitrary axis.
