Anyone here awesome at math by any chance?

I've run into a problem that's kicking my ass.

The provided variables are the cone angle(cA) of a cone that starts at the origin along the Z axis, the vertical angle (vA) of the direction the cone is facing, and a horizontal angle (hA) along with a distance (d) along that angle to reach the xy plane.

With this information I need to find the coordinates on the XY plane where the cone intersects a vertical line generated using the provided horizontal angle and distance. The X is easy to find using Sin(hA) * d.

The cone itself is always originates directly on the Z axis pointing towards the XY plane with a varying vertical angle (vA). Using the cone angle to project what would probably be an ellipses onto the XY plane, I'm looking for the formula used to derive the Y coordinate/s that intersect the vertical line on the X coordinate.

Solution

So, here's what we think is currently the solution.

Provided variables.

hA : horizontal angle

vA : vertical angle

cA : cone angle

d : distance along angle

Necessary variables

x : the length of the line that connects the (0,0) point on the XY plane to the dotted line. Derived by using hA and distance.

x= Sin(hA) * d

z : distance from the origin to (0,0) on the XY plane. Derived by using hA and distance.

z = Cos(hA) *d

cTA : angle from origin to top cone wall. Knowing the angle of the cone's vertex and also knowing that it will be pointing at a point along the y-axis we can determine that subtracting the vertical angle from the cone's angle will give us the angle from the origin to the y coordinate that will be intersected by the cone's wall.

cTA = cA - vA

dYTop: Point on y-axis that is intersected by the top of the cone's wall. Derived by using cTA and z.

dYTop = Tan(cTA) * z

yMid: distance from (0,0) to the cone axis intercept along the y-axis. derived by using vA and z.

yMid = Tan(vA) * z

c: distance from origin to yMid. pythagorean theorem.

c = sqrt(yMid^2 + z^2)

hRadius: horizontal radius of the cone. Derived using cA and c

Tan(cA) * c

vRadius: vertical radius of the cone. Derived by subtracting yMid from dYTop

vRadius = dYTop - yMid

After that we have all the variables needed to input into this formula.

x^2 / hRadius^2 + (y - yMid)^2 / vRadius^2) = 1

Solve for y to get the y points.

height1 = (int)(Math.Sqrt(1 - (x * x) / (hRadius * hRadius)) * vRaduis + yMid);

height2 = (int)(yMid - Math.Sqrt(1 - (x * x) / (hRadius * hRadius)) * vRaduis);

The image above would not have any solutions as the cone's angle isn't large enough to intercept the dotted line at x. I haven't started actually testing this yet but it looks right.... big thanks to @heavyduty32 !

I have been looking at this for like an hour and I just say y=0. I mean just look at your picture. That dotted line intersects with your distance line where there is no y component. I could be completely wrong and this problem needs an integral of some cross products of those lines or something. Or just some parametric or polar coordinates of conic sections. I don't know. Is this for a math class or a programming application or something?

If I am reading this problem correctly, then I believe the answer is y=d*cos(hA)*tan(vA). It looks like tan(vA) would equal y divided by the longer legof that triangle, and because the longer leg is equal to d*cos(hA), then tan(vA)=y/(d*cos(hA)). Solving for y gets d*cos(hA)*tan(vA).

I was an English major.

@rorie said:

Just wanna make sure I have the setup here:

1) Have a cone, fixed size, whose size is known when it's centered over the origin (vA = 0). Presumably it has a circular base in this state.

2) You're rotating that cone STRICTLY ALONG THE Y-AXIS such that the projection of the cone in the X-Y plane becomes an ellipse on the grounds that the base of the cone is no longer parallel to the X-Y plane.

3) hA has nothing to do with the dimensions of the cone, it's simply an arbitrary value such that the dotted line it generates could have 0, 1, or 2 intersections with the cone's X-Y projection.

Sound about right?

@peezmachine: @jediavenger1738: @flacracker: Sorry duders, I think the way I wrote the question was sorta unclear =P

I got a bunch of help from @heavyduty32 . I'm gonna try testing stuff out once I implement it. If all goes well, I'll try to post the solution here... or at least, what I understand of it -_-;;

@godlyawesomeguy said:

@smtdante89 said:

I was an English major.

@rorie said:

I currently am an English major.....so, yeah, fuck this. Good luck to ya, buddy!

In a few months I will graduate as an English major, so I had this same reaction.

I don't think we ever got around to conic sections in any of my trigonometry or calculus classes. That seems like an odd gap in my mathematics education. I should probably check this stuff out on khan academy or something.

@believer258 said:

@godlyawesomeguy said:

@smtdante89 said:

I was an English major.

@rorie said:

I currently am an English major.....so, yeah, fuck this. Good luck to ya, buddy!

In a few months I will graduate as an English major, so I had this same reaction.

I suppose I should rephrase what I said slightly. I only said "was" because I just graduated two months ago myself. So good luck/congrats to you both.

You can't be an artist and a mathematician too. Pick one and be bad at the other.

Are we all English majors?

I tell people I am an English major, because that sounds a lot better than "I have no idea what I am doing with my life oh no please kill me now"

I'm in my periodic differential equations class right now, I'll get it for you when I leave.

Hang on a sec...the way i understood it is that its a cone that is cutting through a vertical plane correct? Therefore, if the origin of the cone is along the z-axis, wouldn't that mean that if one can solve for the x-value, the y-value should be the same, since its the radius of a circle?

@rorie said:

Favorite gif of all time

@smtdante89: That's what I thought at first anyway.

I know what I'm doing (it isn't much).

Isaac Asimov (and pretty much any well-known polymath, for that matter) would like a word with you.

wait... the way you wrote the question is extremely confusing... any way you can just copy/paste the question on here, along with section/class :).

I'm not that great in geometry but start by making a formula for the varying angle and the cone. This isn't a simple x = y ekuation. You need a

x = 0

y = cos(vA) - radius

z = ???

I'm not entirely sure I understand the question. Are you saying that this is not a perfectly circular cone, that it's a cone that is sort of "squished"? And then are you asking, using only hA, vA and d, how do you get the y-coordinate of where the segment that goes along with the vertical angle hits the plane?

In other words, looking at that nice drawing you made, there are two right-angled triangles, one horizontal and one vertical. Two of the segments go along the plane, one vertically and one horizontally. As you said, the horizontal one is d*sin(hA), and you wish to find the length of the vertical one? Am I reading that right?

If so, you can use some standard trigonometry: the horizontal triangle is made up of three segments, with lengths d, d*sin(hA) and d*cos(hA). The d*cos(hA) segment is the one that goes from the origin along the z-axis, hitting the plane at (0,0). That segment is shared with the vertical triangle, so if the length of the segment you're trying to find is Y, then tan(vA) = Y / (d*cos(hA)). Then Y = d*cos(hA)*tan(vA).

Is that what you wanted?

EDIT: somehow I totally missed that @jediavenger1738 had provided this exact answer! Sorry duder, didn't see ya there.

I was awesome at math....

until they started using letters. I checked out from that point forward.

Math is my worst and most hated subject, and this thread reminded me of something that depresses me. Anyway best of luck to you man.

That's what this masters in English I have screams.

Edited the OP with what I've currently got and hopefully a clearer idea of what I'm looking for.

Don't mess with them. They're bad business...

I wish I could =[

I'd love to compare what you've got with what I've got. Ideally I'd like to trim down any equations I can as they'll take up valuable cpu time. Yea, I realize it's written really weird. Unfortunately I'm not an English Major =P

sorry, my illustration was bonkers. I updated. I need to come up with a way to solve for the two points of y given that the hA, vA, cA and distance can always change. So the cone can be angled at any point along y from its origin.

I freaking wish...

No worries. I tried to clear up the question a bit. If you get something different please let me know =]

Yep that updated post with the pictures is like nothing I had envisioned in my head. And the notation is so bad I cant be bothered to read the solution.

@rorie said:

Sums up my feelings pretty nicely.

@rorie said:

Math Rorie

I think you wanna... put the... x... on... that thing.

I'm currently in Calculus and you just blew my mind.

I make a major of English so is am not able for help to you. Sorry for it. You make game in mathmatecks?

huh looks like you got yourself a problem

I am also decent at math and your solution looks good. It's a matter of finding the major and minor axes (a and b) of the ellipse that the cone makes through the xy plane and plopping those values and your value of x into x^2/a^2 + y^2/b^2 = 1 to solve for y values. If the vertical angle of your cone is such that the conic section is a parabola (vertical angle > 90 - 0.5*cone angle) then you will need a different formula for x and y.

Just throwing this out there: math.stackexchange.com

I actually know multiple computer science majors who double majored in Art. And they are great at math. I was surprised too.

Make them stop. They're messing with a universal law.

Wow, I thought the topic of this thread said "meth" instead of math for a second lol.

I'm awesome at making cakes!

So... Why don't you go to a lab after class instead of ask giantbomb video game players how to do your homework? Never crossed my mind to ask anyone here how to trouble shoot a Cisco core switch running in VSS mode (think SLI for switches) from work.