Math Is Fun Forum

Acedemic price? Any sponsering I get at home comes out of my own pocket. lol. I think I'll give myself a scholarship! :-D

Do "visual c++" compilers have graphing programs and stuff? I would assume thats what visual means.

Next we have the class point that has x,y, z and vX, vY member variables. (v for virtual. The points that are used to display the object in 3d)

I might change the virtual coordinates to integers.

This function is for converting from polarform back to rectangular form. It takes x,y coordinates of the center, and the x,y coordinates of the object. (the function assumes the angle is in polar form from the center x, y coordinates that you insert). It multiplies the supplied length by the cosine of the angle to find the x distance, this length is then added to the center x coordinate and the x value is assigned this new coordinate. Same goes with y only you use the sine of the angle and add the result to the center y coordinate. Its really hard to explain in words.

x, and y are not used as paremeters to the function, they are only passed into the functions so their values can be reassigned.

lol. Well anyways I figured I'd post some code now.

Heres another copy of my polarangle function.

:-D Thanks guys. But I'm not sure what you mean by a nontuple post.

Yeah what I need is a graphing program to plot the points in realtime. Right now I have to tediously insert the points into the program and plot them manually. I don't know what sort of program I need though.

Yeah animations would be relatively easy if I had a realtime graphing program and access to a timer function so I can set the speed.

Oh and I can rotate the box easy as pi! ;-) All I have to do is speficy the center of rotation in the center of the box, instread of around the viewer, and rotate the box's points using my rotate function. All I need is a realtime grapher and I could have a lot of fun with this.

Because its an exponential equation. I remember this exact topic being discussed but I can't remember how it went. I'll see if I can find it in my mathbook.

Ok, I used my program to calculate the Vx and Vy coordinates of that same box, with the angle of view rotated 15 degree's down. I also put the box on the front of a flat surface. Then I used autoCAD to plot the points for me.  You can see the box now begins to vanish downward.

Ah... the power of math...

Hmm... yeah I guess if we ever need the sin, cosine, tangent or arctangent of a negative angle, that would occur.

Then what needs to be considered is objects behind you should not be plotted. After the polarangle check you could compare the angle to the object to your angle of view. If its more then 30 degree's greater or less then the angle at which your looking, then don't display it. This and the "set angle of view" function is something I have yet to make.

Of course this only draws dots. A real 3d engie connects the points with lines and fills in the polygons with color. Also shading and other techniques are applied. Also objects usually have to be opaque and "hide" objects that are behind it so you don't see through everything.

Its complicated and like I said I'm reinventing the wheel, but I enjoy trying to figure things out for myself.

Some things to consider now. There should be three global variables for the viewers angle of view on the XZ, YZ, and XY axis. My rotation functions only rotate based on a given angle of rotation, you should instead be able to see "I'm looking that way" and the rotation is applied. If you were looking at 90 degree's on the XZ axis, no rotation would be required. At 91, 1 degree of rotation added, at 100, 10 degree's of rotation added. So I suppose 90 degrees must be subtracted everytime. On the YZ axis, if you are looking at zero degree's, no rotation is required so no adjustments are needed.

Now where was I going with that? Ugh..this is confusing.

To rotate your view by, say, 15 degree's. Yeah you could rotate yourself 15 degree's, but in the case of this program it would be easier to rotate all the objects points around -15 degree's. This would work but theres a problem. The world revolves around you. This is admitably cool but creates problems. An objects location is always changing. I remedied this by using two sets of coordinates. I created a class "point" that holds three coordinatevariables: x, y, and z. And three virtual coordinate variables Vx and Vy. The virtual coordinates are translated and plotted based on the objects real coordinates and the viewers location and angle of view.

First the objects real world coordinates are taken and assigned to temporary variables, these new variables are used in 3d function so the real coordinates are not effected. First the angle to the given point from the viewers location is calculated. (remember my polarangle function? This is what I made it for!) then I use the distance formula ( sqrt (x1 - x2) + (y1 - y2) )  to find the direct distance from the viewer to the point. Now that I have the angle two the object and the distance to the object I know now its polar form. To rotate it, I simply add the negative of the desired roation, and then convert it back to rectangular form. So I remained paralell to the Z axis and rotated the points around me. The virtual points are then assigned the resultant values and the points are plotted. And the real coordinates of the object are completely unchanged.

Again this rotation is done first on the XZ axis (looking left to right) and on the ZY axis (looking up and down) I could also make an XY rotation to flip your view upside down. Easy to do but I don't really need it right now.

Scalling everything in relation to the z distance to the object and rotating the world around you seems pretty restricting and primitive but you can actually use the program without worring about it at all. You can change the viewers coordinates to move around, and rotate your view without a care in the world about how it works. Really the objects are just being translated to the z axis so the perpendicular distance can be easily found.

Heres a quick pic of how the rotation works. (this is down on the XZ axis and ZY axis and the projected)