C2 Math question

Hello, I have a math question for you ;)

I have a rectangle within an object (so that the width/height of the rectangle are defined by object.width * k, object. width * k where k < 1)

I want to be able to pick a random position within the rectangle.

However, the object could be at any angle.

(the origin of the object is the centre point of the rectangle.)

rectangle.x + int(random(-rectangle.width/2,rectangle.width/2))

rectangle.y + int(random(-rectangle.height/2,rectangle.height/2))

— this is what I normally do. The trick lies in the fact that the rectangle can be at any angle.

Well haven't tested, but I would try

rectangle.x+ cos(rectangle.angle)*int(random(-rectangle.width/2,rectangle.width/2))

rectangle.y+ sin(rectangle.angle)*int(random(-rectangle.height/2,rectangle.height/2))

Hmm, newt, that doesn't seem to work...

newt's idea is to sample a value in an unrotated rectangle and then rotate the values arround the center.

Let see then :

sample values inside a rectangle :

x = rectangle.x+random(-rectangle.Width/2,rectangle.Width/2)
y = rectangle.y+random(-rectangle.Height/2,rectangle.Height/2)

xRot = rectangle.x + cos(angle(rectangle.x,rectangle.y,xSample,ySample)+rectangle.angle)*distance(rectangle.x,rectangle.y,xSample,ySample)
yRot = rectangle.y + sin(angle(rectangle.x,rectangle.y,xSample,ySample)+rectangle.angle)*distance(rectangle.x,rectangle.y,xSample,ySample)

x0 = random(-rectangle.Width/2,rectangle.Width/2)
y0 = random(-rectangle.Height/2,rectangle.Height/2)

xRot = rectangle.x + cos(angle(0,0,x0Sample,y0Sample)+rectangle.angle)*distance(0,0,x0Sample,y0Sample)
yRot = rectangle.y + sin(angle(0,0,x0Sample,y0Sample)+rectangle.angle)*distance(0,0,x0Sample,y0Sample)

+On what you want
  Local number randX=0  //random X position withing the rectangle
  Local number randY=0  //random Y position withing the rectangle
  Local number randA=0  //random angle before rotation
  Local number randD=0  //random distance
  -> System: set randX to  random(-rectangle.Width/2,rectangle.Width/2)
  -> System: set randY to  random(-rectangle.Height/2,rectangle.Height/2)
  -> System: set randA to angle(0,0,randX,randY)
  -> System: set randD to distance(0,0,randX,randY)
  -> System: set randX to rectangle.x + cos(randA + rectangle.angle) * randD
  -> System: set randY to rectangle.y + sin(randA + rectangle.angle) * randD

Ah, so its get the rectangle's new angle, generate a random angle, get the difference between those, then generate an offset that is the same for both x, and y.

newt

well, it's really generate a random point and then take it's angle AND distance from the origin.

It's not just a random angle

it's not just a random distance frome the origin

it's not event a random angle and a random distance, 'cause you have to stay within the rectangle boundaries. If you take a random angle and then a random distance from the origin (from 0 to how much?), you can't be sure you are within the rectangle. Angle and distance are linked to discribe a specific point.

So it's really a random point you convert into distance and angle from origin -> rotate -> translate.

Humm, it's working, however at an entirely different point on the map.

Probably my fault, not Yann's ;)

I do rotate layers, but I doubt that really makes much difference.

Be carefull, the layerangle is a bit tricky. I would advise to not use it, especially if you use scrolling. It behave pretty weirdly.

I think that Ash did say somewhere that it's not the layer that rotate but something like, rotate layout -> paste Layer into main canvas -> rotate back. So event layerangle is reversed...

Well it has worked perfectly for me in the past. Also, it is in the same wrong relative position regardless of the layer rotation.

Here's a different way to look at it.

http://dl.dropbox.com/u/666516/randangleimagepoint.capx

As to the layer angle, remember the rotation is counter clockwise, since in essence you are rotating the view.

newt

That looks great! although why do you use numbers 4 and 16 instead of expressions of the size of the box? Basically to adapt this for my own purposes, I need to know how to adjust these constants.

It just divides the rectangle up into the size of the second sprite.

Looks a little better imho, and its easier to get around the issue with hotspots on the second object.

So rectangle width divided by the second objects width/2 *the second objects width.

By using a random angle and random distance the point ends up in a circle, the corners are never selected.

Here is how to have the point random out of the whole area.

http://dl.dropbox.com/u/5426011/examples%209/randpointonrect.capx