bending a rectangle

[kore]

Hi,

here's what I'm trying to do, I want to have a rectangle gradually bend 45 degrees left and then gradually bend 45 degrees right.. I have a bend variable that goes from 0 to 45 back to 0 to -45 back to 0 and so on..

My original idea was to build a rectangle using multiple 4 point polygons, and depending on the variables make the z and x coordinates change depending on the bend.. I haven't been able to make anything decent looking or simulating a bend..

any ideas on an algorithm that could work for this or maybe an easier method ?

[chemdog]

Assuming rw, and rh for rectangle width and height. "angle" is the bend variable in radians.

glBegin(GL_POLYGON);
glPoint2f(0,0); //bottom left
glPoint2f(rw,0); //bottom right
glPoint2f(rw + rh * sin(angle), rh); //top right 
glPoint2f(0 + rh * sin(angle), rh); //top left
glEnd();

This will give a parallelogram, with equal opposite sides. When angle is 0, it is a rectangle. When angle is pi/4, (45 degrees), it is slanted to the right; is -pi/4, (-45 degrees), it is slanted to the left.

[kore]

thanks for the answer... it is not quite what I was hoping to do though.

by bending i mean I want it to be curved, that's why I believe i will need multiple polygons to make up the bent rectangle.

[mw]

You could use OpenGL evaluators for this task

[kore]

thanks I have never heard of these... I will check it out

[kore]

this is what im trying to accomplish :
http://www.koreproductions.com/temp/bentPolygon.jpg

[vegark]

In OpenGL a polygon consists of several streight lines.

It's not possible to curve any "lines" in OpenGL. You need to split the line in several parts. Otherwise the geometry is to coarse.

[kore]

ive now managed to create the arrow with several pieces, and somewhat simulate the bending in it real-time.. It still isn't as good looking as I want but It's a start.

[chemdog]

To make a jello-like rectangle, you can use that single quad bending-code to create a series of stacked rectangles.
In the code angle brackets indicate positions, and addition is in position space; The angle array contains the angle for each slice. sh is the hieght of each slice.

//sh = rh / (last-first+1);
bottomleft = <0,0>;
bottomright = <rw, 0>;
for i = first to last
  offset = <sh*sin(angle[i]), sh >;
  topright = bottomright + offset;
  topleft =  bottomleft + offset;
  DrawRectangle(bottomleft, bottomright, topright, topleft);
  bottomleft = topleft; bottomright = topright;
//endloop

[kore]

wow that worked great.. and much simpler than my original (headache of a method) way..


now, my only problem is with the tapered effect I want with my rectangle... I'm gonna work on this now, but if you have any ideas - let me know..

i really appreciate your help!!