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What's the formula for reflecting an object off a surface?
http://45.55.195.193/viewtopic.php?f=1&t=29848		 Page 1 of 1
Author:  ryry1237 [ Sat Feb 04, 2012 9:12 am ]
Post subject:  What's the formula for reflecting an object off a surface?
I decided to put this in mod making since it's a very useful question when it comes to modding shields and force fields that have realistic reflections and ricochets, and because it's a question I've been thinking over for awhile but haven't gotten anywhere.

A trig question for the math pros out there.

ImageImage
Given the angle of the surface (in radians) and the vector of the incoming ray (in x/y coordinates), what formula should I use to get the coordinates of the resulting ray?
This is assuming that the bounce is perfect and the speed of the ray remains constant.

bonus: What would the formula be if this were to happen in 3-D space (x, y, z coordinates)?
Author:  Mehman [ Sat Feb 04, 2012 10:46 am ]
Post subject:  Re: What's the formula for reflecting an object off a surface?
The outcoming object should have the same angle relative the the surface normal as the incoming object (same as geometrical optics reflection):
Image
Same thing in 3d.

Attachments:
200px-Reflection_angles.svg.png [7.84 KiB]
Not downloaded yet
Author:  Xery [ Sat Feb 04, 2012 11:58 am ]
Post subject:  Re: What's the formula for reflecting an object off a surface?
I'd given out this many many times...

Code:
for target in MovableMan.Particles(Items) do
　local pardist = SceneMan:ShortestDistance(self.Pos,target.Pos,self.mapwrapx);
　local PX = target.Pos.X - self.Pos.X;
　local PY = target.Pos.Y - self.Pos.Y;
　local VX = target.Vel.X - self.Vel.X;
　local VY = target.Vel.Y - self.Vel.Y;
　local judgeX = PX * VX; --to judge if it's moving toward "self" at X.axis
　local judgeY = PY * VY;
　local UV = -((PX*VX) + (PY*VY))/(PX^2 + PY^2);
　local NX = 2*PX*UV + VX; ---new Vel.X of the target
　local NY = 2*PY*UV + VY; ---new Vel.Y of the target
　local paVel = math.sqrt(VX^2 + VY^2);
------------Another Method
--local angP = math.atan(PY/PX);
--local angV = math.atan(VY/VX);
--local paVel = math.sqrt(VY^2 + VX^2);
--local angCA = angP - (angV - angP);
--local flip = (-1 * spX) / math.abs(spX);
　if target.HitsMOs == true and pardist.Magnitude < (58 + (paVel / 12)) then
　　if judgeX < 0 or judgeY < 0 then ---whether it's moving toward "self"
　　　if target.Vel.Magnitude > 5 then
　　　　if target.ClassName == "MOPixel" then
　　　　　self.counterpar = CreateMOPixel(target.PresetName);
　　　　elseif target.ClassName == "MOSParticle" then
　　　　　self.counterpar = CreateMOSParticle(target.PresetName);
　　　　elseif target.ClassName == "MOSRotating" then
　　　　　self.counterpar = CreateMOSRotating(target.PresetName);
　　　　elseif target.ClassName == "AEmitter" then
　　　　　self.counterpar = CreateAEmitter(target.PresetName);
　　　　end
　　　　self.counterpar.Vel.X = 0.8*NX;
　　　　self.counterpar.Vel.Y = 0.8*NY;
--　　　self.counterpar.Vel.X = ((math.cos(angCA) * paVel) + self.Vel.X) * flip;
--　　　self.counterpar.Vel.Y = ((math.sin(angCA) * paVel) + self.Vel.Y) * flip;
　　　　self.counterpar.Pos = target.Pos;
　　　　self.counterpar:SetWhichMOToNotHit(self,-1);
　　　　MovableMan:AddMO(self.counterpar);
　　　end
　　　self.gloweffect = CreateMOPixel("X-CutTool Shield LittleGlow","X-Region.rte");
　　　self.gloweffect.Pos = target.Pos;
　　　target.ToDelete = true;
　　　MovableMan:AddMO(self.gloweffect);
　　end
　end
end


So anything moving toward you that can hit you will be reflect to a realistic direction and can hit the original shooter. It might not be the best solution, but works quite well.
Author:  ryry1237 [ Sat Feb 04, 2012 1:40 pm ]
Post subject:  Re: What's the formula for reflecting an object off a surface?
Xery wrote:
Xery's post

I'm looking at the code and this is what I understand so far

pardist = Distance of object away from self
PX = When positive, target is right of self and vice versa
PY = When positive, target is below self and vice versa
VX = When positive, target is traveling right relative to self and vv
VY = When positive, target is traveling down relative to self and vv
judgeX = When positive, target is traveling away from self based on X value
judgeY = When positive, target is traveling away from self based on Y value
UV = Hmm... don't really get what this is supposed to do.

Code:
local UV = -((PX*VX) + (PY*VY))/(PX^2 + PY^2);

If velocity relative to both self and target = 0, then UV = 0
If UV = 0, then new velocity of X and Y are also 0

If position of y and velocity of y are not considered (1-D perspective)

When PX*VX = positive, UV goes into negatives, target traveling away from self,
When PX*VX = negative, UV becomes positive, and target is traveling towards self (ready to be reflected)
As VX increases, UV also increases proportionally and vice versa
Given that VX remains constant (constant X-coordinate movement),
as PX gets closer to 0 (target gets closer to self X-wise), UV decreases.

Purpose of UV for X coordinate appears to be determining velocity X wise
Image

Same goes for Y coordinate.

Position of both self and target cannot be same otherwise game will divide by 0
Gonna think about this later since there are too many fireworks and screaming car alarms outside.

Attachments:
vector.PNG [1.48 KiB]
Not downloaded yet
Author:  Xery [ Sat Feb 04, 2012 5:17 pm ]
Post subject:  Re: What's the formula for reflecting an object off a surface?
Image
or you can use another method, calculate by trigonometric functions (the "Another Method" lines after "--"), but I try both and fold it run slower than the prev one.
My English is not so good, hope it clear enough though.

Attachments:
图示.png
图示.png [ 38.82 KiB | Viewed 2366 times ]
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