A little trigonometry

[SavannahLion]

For the life of me I can't figure this out. I just can't remember how it's done.

I know the answer is painfully obvious, but it's escaping my search-fu techniques.

And yes, it's arcade related, you'll see eventually.

In the example attachment below, I have a set of three overlapping triangles. Each coordinate is lettered A, B, C with a number indicating which belongs to which triangle. I have the ABC coordinates for ALL of the triangles (I should, I generated those numbers). I can figure out the angles and the lengths and whatever other information I need. What I can't figure out is intersections between the triangles. In the diagram below, it's the intersections outlined by the red circles.

Any trig majors here that can answer that question?

edit: Corrected diagram labeling.

[EvilNuff]

I don't really understand what you are asking...by "coordinate" do you mean x,y coords in a 2 dimensional space?  Are the letters locations or angles?  What do you want from the intersections, the x,y coord location or angles or what?

[SavannahLion]

Oh shuckles. I'm a little rusty that. I've been using ABC interchangeably as x,y coordinates and angles.

To clarify in this case, the ABC values are created and stored as x,y coordinates. I'm trying to figure out the x,y coordinates of the red circled intersections.

[SavannahLion]

Oh   sky. I've been really over-complicating this. I've been treating the problem as whole triangles rather that intersecting lines.

For formula is y = m(x-Px) + Py where Px,Py is a known coordinate and m is the known slope. So for two lines and their intersect, the equation is simply m(x-Px) + Py = m(x-Px) + Py where the left of = is one line and the right is the other line. Solve for x then use x to solve for y.

Now I'm left to figure how to do this proagrammatically(?) without resorting to a math library.

[jennifer]

  Arcade related you say..... I"ve studied it, and concluded, I"t doesn"t appear to be electrical in nature. [unless it"s a flux capacitor]
      If it"s a cab. build, well intense. Maybe, it would be easier to cut the trianges out and intersect them manualy.

[Grasshopper]

It's been a long time since I did anything like this, but from memory, one possible approach might be as follows:

If we assume a point on the line between points A and C is P1 then you can use the following formula to calculate P1:

P1 = A + n(C-A)

If we assume a point on the line between points C1 and C2 is P2 then you can use the following formula to calculate P2:

P2 = C1 + m(C2-C1)

At the intersection between the two lines P1 = P2 therefore:

A + n(C-A) = C1 + m(C2-C1)

Now split the above formula into two (one for the x values and one for the y values):

Ax + n(Cx-Ax) = C1x + m(C2x-C1x)

Ay + n(Cy-Ay) = C1y + m(C2y-C1y)

Now combine the above two formulae to calculate m:

m = [C1x - Ax - n(Cx-Ax) - C1y + Ay + n(Cy-Ay)]/[(C2y-C1y) - (C2x-C1x)]

Now we know m, we can calculate n.

I'd use a spreadsheet to do the calculation.

[SavannahLion]

  Arcade related you say..... I"ve studied it, and concluded, I"t doesn"t appear to be electrical in nature. [unless it"s a flux capacitor]
      If it"s a cab. build, well intense. Maybe, it would be easier to cut the trianges out and intersect them manualy.

It's a software utility. The utility is written in C++ but I'm pre-generating parts of the GUI using Perl + ImageMagick. Originally had some wicked spaghetti code and resorted to Perl's version of OOP to handle the shape manipulation. I'm almost done with the prototype GUI but there's a hidden bug somewhere as the shapes approach virtual "0, 0" in the coordinates. Can't figure out what it is.

I've discovered some disappointing information that abolished my assumptions about DirectX/OpenGL/GDI so I need to do more investigating into that.

In any case, I need to hammer out a couple of left over details and I can compile and release a -nogui version for peer review and debug at least the underlying functions.

To Grasshopper:

I've had one hell of a long weekend so I'm not really in the right mindset to digest your math equations there. If you haven't noticed, I'm rusty on math, I honestly have no clue who any of the presidents are on anything over $5, all I ever do nowadays is pure subtraction.  

Give me some lazy time at work and I'll digest your information.  

[KuraiDori]

What plane of hell did I stumble into?

[SavannahLion]

What plane of hell did I stumble into?

Well... depends on your religion. If you believe in Dante's Hell, then it's probably the 8th circle, 10th ditch. Of course, if you ask the RIAA then it's the seventh ditch. I don't believe any of us really sunk that low. At worst, we're all probably either in the 2nd or 4th circle because most of us want, or have, too many cabs.

I'm almost done with the prototype GUI but there's a hidden bug somewhere as the shapes approach virtual "0, 0" in the coordinates. Can't figure out what it is.

Not that any one cares, but the problem was the box coordinates changes as it approaches 0,0. I was calculating a virtual box with four corners but the coordinates as they arrive towards 0,0 changes into a three corner box (ie a triangle) but my program was expecting a true four corner box. A simple fix was to create a "virtual" corner to create my box for the calculations. Easy peasy.

[KuraiDori]

That's quintessential

The solution as you explained it sounds very similar to the one that I postulated, with the exception of being presented in a coherent format based on sound mathematical formulas that succeeded in explaining and solving the unexpected variances.