How do I find an angle between 2 rays?

[Ethanthegrand14 (Ethanthegrand)]

Hey all. So I’ve been working on a raytracer, and I a want to implement specular lighting. Which makes reflective objects appear more shiny.

Now this is cool and all, but I have no idea how I am suppose to find the angle between 2 rays that I will need to make this work.

How do I do this?

Help would be greatly appreciated as always

My current code:

function ProcessSpecularLighting(IntersectPos, OriginalColor) -- OriginalColor is the color of the pixel on the screen
	local SunRayOrigin = (CFrame.new(IntersectPos, IntersectPos + SunDirection) * CFrame.new(0, 0, 0.1)).Position
	local SunRayDirection = (CFrame.new(IntersectPos, IntersectPos - SunDirection) * CFrame.new(0, 0, 0.1)).Position
	
	local SunLightRay = workspace:Raycast(SunRayOrigin, SunRayDirection, Params)
	
	if SunLightRay then
		local ReflectedSunDirection = SunRayDirection - (2 * SunRayDirection:Dot(SunLightRay.Normal) * SunLightRay.Normal) -- Relfect the direction.
		
		local Shininess = nil -- a percentage from 0 - 1 that is used for the colour combining below
		
		return Color3.new(1, 1, 1):Lerp(OriginalColor, Shininess) -- Merge the two colours depending on the shininess of the angle
	else
		return OriginalColor
	end
end

[IggyDev (Iggy)]

This may help you?

Best way to get the angle between two vectors?

SebastianAurum provided the best way of solving OPs actual problem, but in case someone in the future really does need to find such an angle, here’s how you can do that: First of all, you can’t find an angle between two points. It just doesn’t make any sense, because an angle needs at least three points to be properly defined: a point each on the legs of the angle, and one for the point/knee of the angle. In OPs case, it looks like they’re really asking for the angle between two vectors, which …

[nicemike40]

math.acos(a.Unit:Dot(b.Unit)) will give you the angle between two vectors a and b.

However, I don’t think your reflection code is correct—your Doting the sun vector with itself, when that should be with the surface normal.

[Avallachi]

I believe you do so by finding the dot product.

local angle = acos(SunlightDirection:Dot(-CameraDirection)) -- in radians

[Ethanthegrand14 (Ethanthegrand)]

oh, sorry. Is this correct?

local ReflectedSunDirection = SunRayDirection - (2 * SunRayDirection:Dot(SunLightRay.Normal) * SunLightRay.Normal) -- Relfect the direction.

[apenzijncoolenleuk1 (Apenz1)]

Yes, the dot product of 2 vectors is equal to the product of the length of those vectors times the cos(angle). You can rewrite the formula to get the angle.
In math terms:

Here’s an useful resource:

How to Find the Angle Between Two Vectors: 12 Steps

EDIT: This might be useful if you want to calculate light reflections: Light Reflection Simulation - Roblox Scripting Showcase - YouTube

[CoderHusk]

This isn’t quite the right approach for this case. We want to get rid of the negatives out the dot product we return from these unit rays cause then we basically get a value from 0 to 1 representing the shadow angle. To add on you need to raise this mixture float to some exponent, usually called k. I coded this up quickly in bkcore just to show what i mean

[nicemike40]

Agreed, I was just answering the title’s question and fixing an unrelated bug I noticed (OP edited the post after)

You’re def right though, you don’t really need the actual angle that OP described for specular highlights, just the dot product.