UoM Maths Thread

[hobbitle]

Can anyone help me figure out an algorithm here?  I feel like this should be easier than it is.

Say you have a source of light at point (x,y).
Say that the cone of light emitted from this light source is 2D when viewed from above (so we don't treat it like a 3D cone, its kind of like a triangle that goes on infinitely).

You know two things:
1) The orientation angle in degrees to which the source is pointing (clockwise from the positive y axis).
2) The sweep of the beam (anything from 0 to 360 degrees), which is evenly distributed around the orientation angle.

You are given a location (a,b) and asked to determine if the beam of light falls on that location.  Regardless of distance - this point could be a million points away from (x,y) but if it falls within the cone of the beam then it qualifies as true.

I need an algorithm that can determine whether or not (a,b) is within the sweep of the light source at point (x,y).

My first thought was that you could find the equation for the two lines that describe the 'sweep' and then find out if the point is 'above' or 'below' or 'within' those two lines.  But I can't seem to figure out a way to determine the equation for the lines in a GENERIC way (i.e. for all possible orientations and sweeps).

Anyone got any ideas???

[lzxnl]

Hint. Try using polar coordinates.

Do you have the actual question? Your phrasing is a little bit vague.

[hobbitle]

It's not a question exactly, it's something that needs to occur in order to continue with a programming assignment (where the scope is bigger , this algorithm is just a small portion). I thought it was quite clear, what would you like clarified?
Thanks, I'll have a look into polar coordinates rather than trig.

[lzxnl]

Can anyone help me figure out an algorithm here?  I feel like this should be easier than it is.

Say you have a source of light at point (x,y).
Say that the cone of light emitted from this light source is 2D when viewed from above (so we don't treat it like a 3D cone, its kind of like a triangle that goes on infinitely).

You know two things:
1) The orientation angle in degrees to which the source is pointing (clockwise from the positive y axis).
2) The sweep of the beam (anything from 0 to 360 degrees), which is evenly distributed around the orientation angle.

You are given a location (a,b) and asked to determine if the beam of light falls on that location.  Regardless of distance - this point could be a million points away from (x,y) but if it falls within the cone of the beam then it qualifies as true.

I need an algorithm that can determine whether or not (a,b) is within the sweep of the light source at point (x,y).

My first thought was that you could find the equation for the two lines that describe the 'sweep' and then find out if the point is 'above' or 'below' or 'within' those two lines.  But I can't seem to figure out a way to determine the equation for the lines in a GENERIC way (i.e. for all possible orientations and sweeps).

Anyone got any ideas???

Clockwise from the positive y axis is an interesting way of defining the orientation angle. But come to think of it, that's the only thing slightly weird for me.

Polar coordinates are ideal here because you don't care about distance. In polar coordinates, that just means the theta coordinate is between two numbers. I'm going to try and do this based on my own interpretation of the question.

So, you have a fixed point (x,y) which is the source and you want to see if (a,b) is in the sweep. You'd be best translating this situation to seeing if (a-x, b-y) would be in the same sweep centred at the origin.

The orientation angle wouldn't change here. Let's call it t. As polar coordinates measure the angle from the positive x axis counterclockwise, your orientation angle in polar coordinates would be pi/2 - t. -t because your angle is measured in the opposite direction to polar convention.
Let the sweep be s. If it's distributed evenly, the sweep ranges from theta = pi/2 - t - s/2 to pi/2 - s + s/2
All you need to do now is show that (a-x, b-y) if converted to polar form has an angle in between the range given above.

[hobbitle]

Clockwise from the positive y axis is an interesting way of defining the orientation angle. But come to think of it, that's the only thing slightly weird for me.

Yes, I agree, unfortunately this is the format in which the data is provided to us, so we either have to use it how it is or convert it into something more useful.

Thanks for your thoughts! I'll have a sift through your post properly and see if I can fully understand where you're going with the idea (just in my phone atm).

[rhapsody_]

Hey, sorry for randomly intruding this thread

B.sc jaffy, I'm studying Calculus 1 this semester, I plan on doing Calculus 2 next semester too. If I want to be able to do the Maths and Statistics majors later on, it also compulsory to do Linear Algebra next semester/summer? Not sure if I want to drop one of my other science subjects to do it but I feel I will do better in math than other majors I've had in mind so I'm conflicted 

[lzxnl]

Linear algebra is a must for pretty much any second year maths subjects, so a maths major will require you to do this subject.

[clueless123]

What is a basis for the solution space of a 3x3 identity matrix? 

[kinslayer]

What is a basis for the solution space of a 3x3 identity matrix? 

The solution space is associated with a linear system, not just the coefficient matrix. You need a system of equations Ax = b to talk about a solution space.

The kernel/nullspace of a matrix is the solution set to  Ax = 0. The nullspace of the identity matrix is {0}, ie. the zero vector.

[scribble]

not sure if anyone else in this thread is interested in systems biology, but there's a seminar on in old geology on friday which could be interesting.

[hobbitle]

I'm interested scribs but can't find any info...?

[scribble]

this friday, old geology theatre 1, from 1-2pm. 
its held by MUMS. They run a math related seminar pretty much every friday.

[bonappler]

For Lin Alg students, is the transition matrix the matrix you have to apply to one matrix, let's call it A and to get another matrix called B? If so, what's the difference between a transition matrix and transformation matrix?

[lzxnl]

A transition matrix is a transformation matrix; it is the transformation Tv = v
Its purpose is expressing a vector in one set of coordinates of a particular ordered basis into another set of coordinates in another basis.

[scribble]

i don't understand.