Math, Vectors and Drawing 3D stuff

[Insectoid]

I decided today to put the math I'm being taught to use for once, so I wrote this program (unfinished) that will eventually take in an equation (that part will be messy and is irrelevant to this issue) and display it on a 3D axis. Something's wrong however, and it doesn't draw the axis properly (I will be making it more modular later, so you can adjust the scale and whatnot). As far as I can tell, my math is right. Can anyone figure out what's wrong?

Turing:

type Vector : %Algebraic Vector type     record         x, y, z : real     end record function DotProduct (a, b : Vector) : real %returns the dot product of two vectors     result a.x * b.x + a.y * b.y + a.z * b.z end DotProduct function CrossProduct (a, b : Vector) : Vector %Returns the dot product vector of 2 vectors     var c : Vector     c.x := (a.y * b.z) - (a.z * b.y)     c.y := (a.z * b.x) - (a.x * b.z)     c.z := (a.x * b.y) - (a.y * b.x)     result c end CrossProduct function VectorLength (a:Vector):real %Returns the length of vector a     result sqrt (a.x **2 + a.y **2 + a.z **2) end VectorLength function UnitVector (a:Vector) : Vector %returns the unit vector a vector     var b : Vector     var vector_length := VectorLength (a)     b.x := a.x / vector_length     b.y := a.y / vector_length     b.z := a.z / vector_length     result b end UnitVector function ScalarMultiple (a : Vector, b : real) : Vector %multiplies vector a by scalar b     var c : Vector     c.x := a.x * b     c.y := a.y * b     c.z := a.z * b     result c end ScalarMultiple function Proj (a:Vector) : Vector %returns the projection of a 3d vector onto a 2d plane     var b : Vector     var c : Vector     b.x := 1     b.y := 1     b.z := 0     c := ScalarMultiple (b, DotProduct (a, b)/(VectorLength(b)**2))     result c end Proj proc DrawDot3D (a : Vector) %draws a dot at the end of vector a    var projection : Vector := Proj (a)     Draw.Dot (round (projection.x), round (projection.y), black) end DrawDot3D proc DrawLine3D (a, b : Vector) %draws a line from vector a to vector b     var projA := Proj (a)     var projB := Proj (b)     Draw.Line (round (projA.x), round (projA.y), round (projB.x), round (projB.y), black) end DrawLine3D proc DrawAxis     var xAxisTop : Vector     var xAxisBottom : Vector     var yAxisTop : Vector     var yAxisBottom : Vector     var zAxisTop : Vector     var zAxisBottom : Vector         xAxisTop.x := 350     xAxisTop.y := 0     xAxisTop.z := 0         xAxisBottom.x := 50     xAxisBottom.y := 0     xAxisBottom.z := 0         yAxisTop.x := 0     yAxisTop.y := 350     yAxisTop.z := 0         yAxisBottom.x := 0     yAxisBottom.y := 50     yAxisBottom.z := 0         zAxisTop.x := 0     zAxisTop.y := 0     zAxisTop.z := 350         zAxisBottom.x := 0     zAxisBottom.y := 0     zAxisBottom.z := 50         DrawLine3D (xAxisTop, xAxisBottom)     DrawLine3D (yAxisTop, yAxisBottom)     DrawLine3D (zAxisTop, zAxisBottom) end DrawAxis DrawAxis

Yes, the DrawAxis function is really messy at the moment, that was just a hackjob to make sure my math worked. Which is doesn't. I think it might have something to do with my Proj function, though I can't for the life of me figure out what's wrong. Maybe it's 'cause I used the equation to project a line onto another line rather than a plane? I dunno if it makes a difference.

[andrew.]

Are you guys already learning vectors in calculus!? We are so behind...

[Insectoid]

We're haven't done calculus yet, so you're not behind (just doing things out of order).

[Kharybdis]

learning calculus before vectors is better than learning vectors beforehand because it ties in with functions

[Insectoid]

How about we stop talking about the school system and figure out what's wrong with my code?

[Zren]

Are you trying to add perspective/camera?

If you remove the modifications in the proj() (for now just have result a), it works perfectly for a simple 3D object to 2D.

[Insectoid]

It doesn't draw the axis correctly when I just result a.

I conclude that it is in my formula for proj() that my error lies.

[Zren]

What's it suppose to look like?
You've got something up and down the y, x axis. and the dot at (0, 0) representing the z-axis line.

[Insectoid]

Ah, I had a little brainfart. My coordinates for the axis were wrong. Lol. Anyway, the proj() function will be needed for when rotation happens, and I can't just result A (Only reason that works now is because drawing things only looks at the X and Y values, which are already accurate for the current perspective. As soon as rotation comes in, it will break down).

[Insectoid]

So, I figure I need to calculate the equation for the plane representing the screen (which can change depending on the screen's orientation), then project the image onto that plane. I'll fix this up as I progress in Calc & Vectors.

[Insectoid]

Sorry for the multiposting, but I've had a mind-breakthrough.

So, I figure to simulate rotation, I'm going to have a 'screen-plane' which, hence the name, is a plane representing the screen. Rather than rotating the axis, I'll be rotating this plane and projecting vectors/points onto the rotation, and then drawing the projection based on X and Y coordinates (Z will be ignored, as X and Y will already correspond to their screen locations and are the only things I need). The projection 'rays' (the line from the original point to the projected point) should be normal to the plane. I figure this will increase efficiency in both coding and runspeed, as I'll be able to generate a list of points from an equation once (which I expect to be the slowest part of the program) and then project those points onto the plane. Really, I'm switching out adjusting points for adjusting the orientation of the projection plane (which should be a lot faster).

Anyway, I still have the problems of projection onto the plane, representing the plane in code and rotating that plane. I'm not a math genius, so I may need a good bit of help with that. I don't even know where to start.

[SNIPERDUDE]

I'd be very interested in seeing a demo on this, I haven't taken such an approach before.