Spheres and Cones - Page 3

munin · 08-23-2010, 02:02 PM

Each level of Area Effect multiplies volume by 4, so if you're going to use a level of Area Effect to increase the height of the effect, shouldn't you multiply by 4, not 2?

Langy · 08-23-2010, 05:30 PM

Agreed, Munin. I'd already decided that 'doubles vertical area of effect' was going to be a +25% enhancement - that makes 'doubles radius and quadruples vertical area of effect' a +100% enhancement. I'd then make 'area is a sphere instead of a cylinder' a flat -20% limitation or something like that. I certainly wouldn't charge more to double the vertical area of effect than I would to double the horizontal area of effect!

munin · 08-23-2010, 08:03 PM

The volume of an Area Effect with respect to its cost is a base 16 exponential progression -- every +1 to cost (+100%) multiplies the volume by 16. From this we can estimate the enhancement or limitation cost for any volume multiplier. For example, multiplying volume by 4 would be an enhancement equal to logarithm base 16 of 4, or log(4)/log(16) = 0.5 (i.e., +50%, what we would expect for a doubling of a cylinder's radius).

Using this method, multiplying an Area Effect volume by 2 (such as doubling its height) would be a +25% enhancement (as one might expect), and multiplying by 2/3 would be about a -15% modifier (log(2/3)/log(16) = -0.146).

From this we could say that a 2-yard radius "Sphere Effect" is worth +35%* (two-thirds the volume of a cylinder 4 yards in diameter and 4 yards high, an initial area effect), and that each additional doubling of the sphere's radius is worth +75% (doubling the sphere's radius multiplies its volume by 8, and log(8)/log(16) = 0.75, or +75%).

* though you have to be careful about applying negative modifiers to the initial 2 yard radius, because by this method a 1-yard radius area effect would be a +0% enhancement (yay, logarithms!), when in fact it's +25% (p. DF5:9). Going from a 1 yard radius at +25% to a 2 yard radius at +50% is a base 64 exponential progression for volume, which would make ×2/3 worth about -10%, not -15%. But -15% is close enough and keeps things consistent for larger volumes in the base 16 progression.

Ejidoth · 08-23-2010, 08:13 PM

The problem with basing it purely on volume is that volume alone is a poor gauge of utility. After all, if you could design effects of any shape as long as the volume is right, you could cut out the top 2 yards of the default area effect and cover twice the radius for almost all purposes as a mere +0% feature. Any good powergamer would take that option in a heartbeat, and would basically point and laugh at any poor fool that took the 'same volume as equivalent area effect' version of a sphere.

The 'ground level' 2-dimensional area of an area effect is where most targets will be, and as such is far more important than the area's 3-dimensional volume, as has been pointed out earlier on this thread.

08-23-2010, 02:02 PM	#21
munin Join Date: Aug 2007 Location: Vermont, USA	Re: Spheres and Cones Each level of Area Effect multiplies volume by 4, so if you're going to use a level of Area Effect to increase the height of the effect, shouldn't you multiply by 4, not 2?

08-23-2010, 05:30 PM	#22
Langy Join Date: May 2008 Location: CA	Re: Spheres and Cones Agreed, Munin. I'd already decided that 'doubles vertical area of effect' was going to be a +25% enhancement - that makes 'doubles radius and quadruples vertical area of effect' a +100% enhancement. I'd then make 'area is a sphere instead of a cylinder' a flat -20% limitation or something like that. I certainly wouldn't charge more to double the vertical area of effect than I would to double the horizontal area of effect!

08-23-2010, 08:03 PM	#23
munin Join Date: Aug 2007 Location: Vermont, USA	Re: Spheres and Cones The volume of an Area Effect with respect to its cost is a base 16 exponential progression -- every +1 to cost (+100%) multiplies the volume by 16. From this we can estimate the enhancement or limitation cost for any volume multiplier. For example, multiplying volume by 4 would be an enhancement equal to logarithm base 16 of 4, or log(4)/log(16) = 0.5 (i.e., +50%, what we would expect for a doubling of a cylinder's radius). Using this method, multiplying an Area Effect volume by 2 (such as doubling its height) would be a +25% enhancement (as one might expect), and multiplying by 2/3 would be about a -15% modifier (log(2/3)/log(16) = -0.146). From this we could say that a 2-yard radius "Sphere Effect" is worth +35%* (two-thirds the volume of a cylinder 4 yards in diameter and 4 yards high, an initial area effect), and that each additional doubling of the sphere's radius is worth +75% (doubling the sphere's radius multiplies its volume by 8, and log(8)/log(16) = 0.75, or +75%). * though you have to be careful about applying negative modifiers to the initial 2 yard radius, because by this method a 1-yard radius area effect would be a +0% enhancement (yay, logarithms!), when in fact it's +25% (p. DF5:9). Going from a 1 yard radius at +25% to a 2 yard radius at +50% is a base 64 exponential progression for volume, which would make ×2/3 worth about -10%, not -15%. But -15% is close enough and keeps things consistent for larger volumes in the base 16 progression.

08-23-2010, 08:13 PM	#24
Ejidoth Join Date: Jul 2009	Re: Spheres and Cones The problem with basing it purely on volume is that volume alone is a poor gauge of utility. After all, if you could design effects of any shape as long as the volume is right, you could cut out the top 2 yards of the default area effect and cover twice the radius for almost all purposes as a mere +0% feature. Any good powergamer would take that option in a heartbeat, and would basically point and laugh at any poor fool that took the 'same volume as equivalent area effect' version of a sphere. The 'ground level' 2-dimensional area of an area effect is where most targets will be, and as such is far more important than the area's 3-dimensional volume, as has been pointed out earlier on this thread.