pyramid of death

Has anyone figured out what the boundaries for a pyramid are?

Hee hee hee. This is really ghastly, I know. I've been avoiding writing this code for a while because it's distressing

What I intend to do is:

1. Bound the bottom of the pyramid (this is easy because it's a plane parallel to the xz plane).

2. Bound the top of the pyramid (again, easy, the height is all at point {0,1,0})

3. Bound on a plane parallel to the hypotenuse of each face. My thinking here is based on 2D thinking. If you were inside a right-angled triangle, you'd have to test every point to see if was on the inside of the hypotenuse. The mathematics don't appear to be that hard. Now you just have to "pretend" you're in 2D, calculate the hypotenuse, and then check whether you've crossed it or not. I hope it works.

I found something else that might be useful. Apparently, the dot product of two vectors defines the cosine of the angle between those two vectors. If you're working in 2D and you want to determine if a point is inside a convex polygon, then you define a vector for each edge of the polygon, and a vector from your point to the first vertex of the edge. The dot product of these two vectors is the cosine of the angle between them, and if all the dot products so calculated are positive, then the point is inside the polygon.

This might help. I haven't figured out exactly how, though.

hehehe....

its actually really simple - it clicked for me last year after a doodle or two - here's a hint:

thinking in 2d is the right place to start.
a pyramid has 45degree sides.
one 45 degree triangle has sides eg 1,1,hypoteneuse
another has 0.5,0.5,another hypoteneuse

any more and I may as well just give the answer. Geometry aside, the maths for the actual collision detection is nothing beyond what you learnt in primary school - forget dot products and trig.

oops

went back and checked up on my code and actually did it a bit differently - the hint above will still get you thinking in the right way though... the thing about 45 degrees might be wrong, but the principle of thinking in terms of similar triangles of different sizes is on the right track.

used the equation y = mx +c

worked out the m of the pyramid boundaries.
if the particle moved away this m value it would be out of the pyramid.

Ah. I did something different. Mr Halland sent me a mail in which he guided me towards the equation of the plane. He said to try to express it in terms of the y value, but I did it differently. Equation of the plane is Ax+By+Cz+D. If you plug your point's {x,y,z} into this and it is <= 0, you're outside the pyramid. Works fine.

Im drawing a cylinder with GLUquadric* t = gluNewQuadric();
gluQuadricDrawStyle (t, GLU_LINE);
gluCylinder(t, 1.0f, 1.0, 2, 50,1);

how do you draw so the centre of the cylinder is coord(0,0)

Gave up on the vertical viewing angle couldnt stop it from being shaky.

Push the matrix, translate the cylinder, pop the matrix. That's what I did.

Hi Vaughn,

You may have got it by now but I used gltranslatef()

thanks

hmmm... this thread seems to have changed topic, but my very poor hint earlier was just trying to point out that similar triangles have the same ratio between the two sides that make up the right angle... so once you have the vertical position of the particle you can very quite simply determine the maximum horizontal co-ord at that point...

to get the ratio we divide maximum height by half a side length (half because we want a right angled triangle around y-axis) ie 2/1=2
(because the pyramid stays the same you might as well assign the ratio as a constant)

now shift our y-value so that we measure "height" in the pyramid from the top (point at the apex=0 and at base = 2) ie 1-yval.

now to get the maximum horizontal simply divide our "height" by the ratio ie ratio/height=max.

if the horizontal values are more than max (or less than -max) just move them back inside with a while loop decremeting by a small amount.

so say we have a point (x,0,z)
height is 1-0=1
max value is 1/2=0.5
while(x>max)x-=0.001;
while(x<-max)x+=0.001;
etc.

whole thing is 5 lines of simple code... and don't forget to massage the y value into the -1...1 range first.

Hi Guys. The idea given br "Tripod" above is correct.
When we halve the height, we get half the pyramid and also the x and z range is also halved. Just decrease the x and z range by the decrease in height(y) and we get our boundaries.

Just draw a diagram on paper and play around. Thats how I fugured all these out.

Since the due date for the assigment has passed, here are some code
to help you guys out:
(I just hope this is not agaist any rules. If it is, I am sorry.)



bool TestPtInCube( point3 pt, GLfloat ln )
{
if ((pt[0] > 1) | (pt[0] < -1) | (pt[1] > 1) | (pt[1] < -1)
| (pt[2] > 1) | (pt[2] < -1)
| ln > partLngth[partnumber]) // also check Length

return false;
else
return true;
}


bool TestPtInCylinder( point3 pt, GLfloat ln )
{
float Ax;
float Ay;
Ax = pt[0];
Ay = pt[1];
if ((sqrt((Ax * Ax) + (Ay * Ay)) > 1.0) // sqrt of the sum of sqrs of sides
| (pt[2] > 1.0) | (pt[2] < -1.0) // the end sides
| ln > partLngth[partnumber]) // also check Length

return false;
else
return true;
}


bool TestPtInPyramid( point3 pt, GLfloat ln )
{
float Ax;
float Ay;
float Az;
float yLen;
Ax = pt[0];
Ay = pt[1];
Az = pt[2];
// The base length is always the length of pt(y)
// Only in the case where height = len of side = same len sides = (for square bases)
// When we move halfway from top pt, the base at pt will also be halved.
yLen = 2 - (Ay + 1); // Calc Len of y pt away from pt(0,1,0)
yLen = yLen /2; // since zero is mid-pt - half on either side of center.
// ie. when Len y = 1, the base is x = -0.5 to 0.5 = Len 1 = Len y. Same for z.
if ((Ax < -yLen) | (Ax > yLen) |
(Az < -yLen) | (Az > yLen) |
(Ay < -1) | (Ay > 1))
return false;
else
return true;
}

bool TestPtInContainer( point3 pt, GLfloat ln )
{
if (ContainerID == 1) return TestPtInCube(pt, ln);
if (ContainerID == 2) return TestPtInCylinder(pt, ln);
if (ContainerID == 3) return TestPtInPyramid(pt, ln);
}

Maybe you guys can help me out with the other algebra stuff like determinants and when and why and how do we get the rotation / scaling searing matrices or can I just by-heart them because they do never change?
Thanks

Determinants are beyond the scope of the course (unless they changed it since last year)... probably good to figure out in the long run, but you don't need them yet.

the matrices are just facts so yes, "by heart", if you think its worth the effort as you will barely ever use them - at least for the course. OGL just uses them internally to do the transforms for you. Seem to remember figuring out some scheme to memorise them for them for the exam, but for most purposes you can just look them up for now. If you ever get into writing your own 3d engine they are good to know though.

AND FAR BETTER NOT TO CROSS THREADS ON FORUMS -
start a new thread and people who aren't intersted in pyramids might answer you, and info posted in them is easier to find later on.