[Math question] Finding the Size of a shadow

Dareoon Dalandrove · May 20, 2003

I was wondering if anyone can help me. I need to figure out a way to find the size a shadow that a person or creature will cast in relation to a light source. At first I thought it would be similair to the equation for light intensity. I= K/d (squared) but I know that it is wrong.

mmadsen · May 20, 2003

This is a trigonometry problem. At noon (light directly above), you cast no shadow (more or less). At dawn or dusk (light on the horizon), you cast an infinitely long shadow (on the floor, pretending it's a perfectly flat plane). At halfway between dawn and noon or noon and dusk, you cast a shadow equal to your height.

Calculate the tangent of the light-source's angle with respect to the shadow-surface, and multiply that by the subject's height.

Tiefling · May 20, 2003

mmadsen said:
Calculate the tangent of the light-source's angle with respect to the shadow-surface, and multiply that by the subject's height.

I'm may be wrong, but wouldn't it be the inverse tangent of the light source's angle?

Saeviomagy · May 21, 2003

1. What do you mean by 'size'? Length? Area?

2. What sort of surface is the shadow cast on? Flat? Angular? What angle is it in relation to the caster?

3. What sort of light source? Diffuse? Point? Where is it?

You need to give us the information you're starting with, and the result you need, or else we're going to have to fully spec out a raytracer for you.

Dareoon Dalandrove · May 21, 2003

What do I mean by size, lenght, area. Well that is always going to change. I was reading the spell Shadow Strike from Relics and rituals and it says that you cast the spell and turn the subjects shadow into a conduit for dealing damage. I could find no rules governing the size of the subject shadow. So wanting to take full advantage of the spell, and of course not wanting to get the smake down each time I use it, I need to find out how to figure out the lenght of shadow a person or creature casts.

Hypersmurf · May 21, 2003

The Size of a Shadow?

Monster Manual says "Medium".

-Hyp.

Maudlin · May 22, 2003

Technically, light goes on forever, in a straight line. So, without any further obstruction, a lateral light-source illuminating an object would cast a shadow reaching to the horizon, until the curvature of the planet interferes with its (projected) path.

That's a totally useless answer from a gaming perspective, though, so just pick a number

Utrecht · May 22, 2003

Dareoon Dalandrove said:
What do I mean by size, lenght, area. Well that is always going to change. I was reading the spell Shadow Strike from Relics and rituals and it says that you cast the spell and turn the subjects shadow into a conduit for dealing damage. I could find no rules governing the size of the subject shadow. So wanting to take full advantage of the spell, and of course not wanting to get the smake down each time I use it, I need to find out how to figure out the lenght of shadow a person or creature casts.

For Simplicity sake, I wold use the following:

Late Morning/Early Afternoon Shadow occoupies 5 ft square

Early Morning/Late Afternoon - Shadow occupies 10 ft square

Now if you want to get complicated:

Shadow length = heighth of object*SIN(Angle of Sun off of Horizon)

MarauderX · May 22, 2003

Completely disregarding longitude, latitude and time of day, as well as all other geometry, as a DM I would go with a simple factor based length of shadow.

Length = Height x (0.25 per hour before/past noon)

For example, 6 foot character stands around at 10 AM.

L=6x(0.25x2) = 3 foot shadow.

I would only include 6 AM to 6 PM, so the maximum factor would be 1.5xheight. Also if you are farther north of the equator you could add to the equation a bit:

Length = Height x (0.25 + 0.25 per hour before/past noon)

So at noon that same 6 foot guy now has a shadow of 1.5 feet at noon, and 9 feet at 6 AM/PM.

And in the extreme north the shadows would be even longer so have fun telling your DM that your shadow extends to the horizon at dawn and dusk. Your DM might say "it most certainly does, however it is so diffuse and weak that you can only use the first X feet of length." Or at least that's what I might say.

If you have another light source, say indoors, and you want to find your shadow on a wall, I would use some simple geometry to get a rough idea. The shadow will change size dependant on distance of the light source from the character and distance of the light source from the wall or floor. Have fun doing the math.

Drawmack · May 22, 2003

The tip of the shadow will form a right triangle with the light source.

Taking that fact into account, the object's highest point will also form a right triangle with the tip of it's shadow.

It's all relative to the angle of the light object from the object's heighst point.