[RESOLVED] math help needed.. how to calculate points of a rectangle?

[lab1]

Hello,

I have a few pieces of information:

x, y point number 1
x, y point number 2
angle where point 1 would intersect with point 2
width of rectangle
length of rectangle

so here is a simple example for the following values:

x1, y1 = (0,0)
x2, y2 = (4, 0)
angle = 90 degrees
width = 4
length = 5


so my rectangle points for this would be:

upper left: (4, 2)
lower left: (4, -2)
upper right: (9, 2)
lower right: (9, -2)

How can I write code to compute these points with the information given? Can someone provide example code?

Thanks!

[D_Drmmr]

How can I write code to compute these points with the information given? Can someone provide example code?

There's no point writing code if you don't have an algorithm. First find an algorithm, then convince yourself that it works and then worry about how to implement it.

[lab1]

yeah I am bad at math so I was asking for help with an algorithm. can you help?

[monarch_dodra]

Hello,

I have a few pieces of information:

x, y point number 1
x, y point number 2
angle where point 1 would intersect with point 2
width of rectangle
length of rectangle

What? I've never heard of a point intersecting with another.

so here is a simple example for the following values:

x1, y1 = (0,0)
x2, y2 = (4, 0)
angle = 90 degrees
width = 4
length = 5


so my rectangle points for this would be:

upper left: (4, 2)
lower left: (4, -2)
upper right: (9, 2)
lower right: (9, -2)

How can I write code to compute these points with the information given? Can someone provide example code?

Thanks!

Could you explain please? You make it look like it is obvious, but this makes no sense to me.

PS: As a matter of fact, successfully explaining it is 50% of the work

[lab1]

Hello,

Sorry about my lack of explanation. What I meant is the angle of a perpendicular line at point 2, if a line connected points 1 and 2. Here is a picture below:

                                        /
                                       /
x1, y1=(0,0)                        c /       
         *--------------------------*/
                    x2, y2 = (4,0)  /
                                   /
                                  /

So the points are the *'s. The angle is where the 'c' is. So in my drawing the angle is a bit greater than 90 degrees.

In my previous example I gave the angle as 90 degrees. So, it would look like this:

                                    |
x1, y1=(0,0)                      c |       
         *--------------------------*
                    x2, y2 = (4,0)  |
                                    |

See what I mean now?

Thanks!

[monarch_dodra]

Sounds like a trig problem to me.

Lets' make it simpler:

Assuming you have
P1(0, 0)
P2(x, 0)
The first segment is horizontal.
And the rectangle width and height are known (as W and H).
You want to place your rectangle at an angle theta to the horizontal line.

Take out a piece of paper and try to find the coordinates of the lower left angle. Draw as much as you want, and replace with numbers if you find it helps.

Once you find the formula, the fun begins.

PS. It's not that I don't want to give it to you, but if you can't find it on your own, you stand no chance at coding it. You need to do the effort, and then we'll help.

[lab1]

The problem is it is more complex that that. The x2, y2 point could be anywhere.. to the left of, to the bottom of, etc. of course I already did the paper exercise, but the angle could also bee something different then 90 degrees. I put hours of effort into this before I posted.

[superbonzo]

if I understand what you mean then it should be

"upper left": z2 - M(-t)(z2-z1) * w / ( 2|z2-z1| )
"lower left": z2 + M(-t)(z2-z1) * w / ( 2|z2-z1| )
"upper right": z2 - M(-t)(z2-z1) * w / ( 2|z2-z1| ) - M(-t-pi/2)(z2-z1) * h / |z2-z1|
"lower right": z2 + M(-t)(z2-z1) * w / ( 2|z2-z1| ) - M(-t-pi/2)(z2-z1) * h / |z2-z1|

where z1, z2 are the two points, || is the usual morm, t is the angle as you defined it and M(t) is the usual rotation matrix:

cos(t) -sin(t)
sin(t) cos(t)

it should be straightforward to translate this into coordinate-wise formulas and then into code...

[lab1]

can anyone provide code for this? I am totally lost here.. I think code will help me better understand it

Thanks

[monarch_dodra]

IF you know matrixial calculation, and you understand what a rotational matrix is, than superbonzo already gave you the formula.

If not, you'll have to expand the 2D formula to 2x 1D formulas.

I understand your P2 could be anywhere. When tasked with a hard problem you don't know how to tackle, always start by simplifying it to something you can handle, and then add in more complexity. That said, superbonzo's formula works for everything you need.

To do matrixes in C++, you can either write them yourself (not too recomended), use a widelly used public library (is this for school, it might not be acceptable).

A third solution (I would recommend) would be to use complex algebra. Just use superbonzo's formula, but replace M(t) with ( cos(t) + i sin(t) ).

[lab1]

So I can just replace "M(-t)" with "(cos(t) + i sin(t))" ? But what is 'i' here?

Also how do I represent somethig like: "2|z2-z1|" in code?

Thanks!

[Lindley]

So you don't know matrix math or complex numbers?

Well, the expression can be expanded out easily enough, that's just the compact form.

[lab1]

hmm complex numbers, ok.. so in C++ code I would replace M(-t) with: cos(t) + sqrt(-1)*sin(t) ?

and to do the norm I would using the complex header file and just:

2*norm(z2-z1) ?

But I guess I am abit confused because the norm() doesnt take an x,y point, but rather just an integer.. right?

Also, since I dont know how to do matrix calculations in C++, can someone suggest how to expand it to 2 1D functions?

Thanks

[monarch_dodra]

No, you'd use a an object called complex:

std::complex myComplexNumber(cos(t), sin(t));
or
std::complex myComplexNumber = polar(rho, t);

You can also use abs for calculating |z2-z1|. You could also simplify superbonzo's formula with a bit of arg:

std::complex upperLeft = z2 + polar( w/2, arg( z2 - z1 ) + t);

PS: and it's c++ code too. Here, z2 and z1 are the complex coordinates of P1 and P2. t is a real number representing theta, expressed in radians.

Since you didn't tell use how t was oriented, this formula may or may not generate the desired result.

[lab1]

"Since you didn't tell use how t was oriented, this formula may or may not generate the desired result. "


What exactly do you mean here? Did my pictures not explain where t is located?

Thanks