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<blockquote data-quote="Anax" data-source="post: 4320983" data-attributes="member: 19868">If you want to get really technical about things:1) In 4E-space, the distance metric is Delta = max(Delta_x, Delta_y).&nbsp; (In Euclidean space, it's Delta = (Delta_x^2 + Delta_y^2)^0.5.&nbsp; In taxi-cab space it's Delta = Delta_x + Delta_y.)2) Although it is expressed in terms of &quot;an n-x-n square&quot;, a 4E blast covers a circle in 4E space.&nbsp; The circle has diameter n.3) No point within the area of a circle of diameter n is further away than n from any other point within that circle.4) Therefore the only figure that describes a circle in 4E-space is a figure that would describe a square in Euclidean space which has sides parallel to the x- and y-axes.&nbsp; Specifically:[code]n=3 n=5&nbsp;&nbsp; n=7XXX XXXXX XXXXXXXXXX XXXXX XXXXXXXXXX XXXXX XXXXXXX&nbsp; &nbsp; XXXXX XXXXXXX&nbsp; &nbsp; XXXXX XXXXXXX&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; XXXXXXX&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; XXXXXXX[/code]The following figure is not a circle (blast) of diameter 3 in 4E-space:[code]XXXXXX&nbsp;XX&nbsp; X[/code]It covers the same area (number of squares), but the top left corner is more than 3 away from the lower right corner.&nbsp; Therefore it cannot be inscribed within a circle of diameter 3.&nbsp; It is not a 4E-circle.The following figure is not a circle (blast) of diameter 3 in 4E-space:[code]&nbsp;X&nbsp;XXXXXX&nbsp; X[/code]It covers less squares of area than a 4E-circle would (eight instead of nine squares).&nbsp; However, it still cannot be inscribed within a circle, because the top &quot;point&quot; is more than three squares of distance away from the bottom &quot;point&quot;.Because blast areas in 4E are circles under the distance metric in 4E, there is no way to &quot;rotate&quot; them which does not result in exactly the same figure.&nbsp; They are perfect circles in 4E space and any attempt to rotate them that results in a different figure is based on translation into a different spatial measurement system--and specifically, it involves transforming the figure in a faulty way.If you want to cover different kinds of areas, I strongly suggest that you house-rule a change in coordinate systems.&nbsp; The best choice would probably be to a faux-Euclidean space in which diagonal movement costs 1.5x horizontal or vertical movement.&nbsp; For simplicity, you can say it alternates between one and two times normal movement.&nbsp; With that definition, the following are valid blasts (remember: the first diagonal is 1 space, the second is two, etc.&nbsp; This is counting from the center for my figures):[code]n=3 n=5&nbsp;&nbsp; n=7XXX&nbsp; XXX&nbsp; &nbsp; XXXXXX XXXXX&nbsp; XXXXXXXX XXXXX XXXXXXX&nbsp; &nbsp; XXXXX XXXXXXX&nbsp; &nbsp;&nbsp; XXX&nbsp; XXXXXXX&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; XXXXX&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; XXX[/code]Taxi-cab space is also a possibility--this is a space where you cannot move diagonally, only horizontally or vertically.&nbsp; The following are circles in taxi-cab space:[code]n=3 n=5&nbsp;&nbsp; n=7&nbsp;X&nbsp; &nbsp; X&nbsp; &nbsp; &nbsp; XXXX&nbsp; XXX&nbsp; &nbsp; XXX&nbsp;X&nbsp; XXXXX&nbsp; XXXXX&nbsp; &nbsp;&nbsp; XXX&nbsp; XXXXXXX&nbsp; &nbsp; &nbsp; X&nbsp; &nbsp; XXXXX&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; XXX&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; X[/code]Either of these geometries are much more amenable to cone-shaped areas than 4E's geometry.&nbsp; I suspect that's part of why they left cones out of the system completely--they just don't make sense.A further alternative that stays within 4E's geometry but allows for slightly more control would be to allow the shape of a blast to cover the caster's square (without actually damaging the caster):[code]OXX XXXXXX OXXXXX XXX[/code]My opinion is that allowing these two options for the casting shape increases the flexibility of blasts, but only to a very slight degree.&nbsp; The main increase in power here comes from the right figure, in which the caster can hit five adjacent enemies.&nbsp; If you forbid this option, all of the other shapes (including the left variant above) only allow the caster to hit three adjacent enemies--all of the other enemies must be further away.</blockquote>

[QUOTE="Anax, post: 4320983, member: 19868"] If you want to get really technical about things: 1) In 4E-space, the distance metric is Delta = max(Delta_x, Delta_y). (In Euclidean space, it's Delta = (Delta_x^2 + Delta_y^2)^0.5. In taxi-cab space it's Delta = Delta_x + Delta_y.) 2) Although it is expressed in terms of "an n-x-n square", a 4E blast covers a circle in 4E space. The circle has diameter n. 3) No point within the area of a circle of diameter n is further away than n from any other point within that circle. 4) Therefore the only figure that describes a circle in 4E-space is a figure that would describe a square in Euclidean space which has sides parallel to the x- and y-axes. Specifically: [code] n=3 n=5 n=7 XXX XXXXX XXXXXXX XXX XXXXX XXXXXXX XXX XXXXX XXXXXXX XXXXX XXXXXXX XXXXX XXXXXXX XXXXXXX XXXXXXX [/code] The following figure is not a circle (blast) of diameter 3 in 4E-space: [code] X XX XXX XX X [/code] It covers the same area (number of squares), but the top left corner is more than 3 away from the lower right corner. Therefore it cannot be inscribed within a circle of diameter 3. It is not a 4E-circle. The following figure is not a circle (blast) of diameter 3 in 4E-space: [code] X XXX XXX X [/code] It covers less squares of area than a 4E-circle would (eight instead of nine squares). However, it still cannot be inscribed within a circle, because the top "point" is more than three squares of distance away from the bottom "point". Because blast areas in 4E are circles under the distance metric in 4E, there is no way to "rotate" them which does not result in exactly the same figure. They are perfect circles in 4E space and any attempt to rotate them that results in a different figure is based on translation into a different spatial measurement system--and specifically, it involves transforming the figure in a faulty way. If you want to cover different kinds of areas, I strongly suggest that you house-rule a change in coordinate systems. The best choice would probably be to a faux-Euclidean space in which diagonal movement costs 1.5x horizontal or vertical movement. For simplicity, you can say it alternates between one and two times normal movement. With that definition, the following are valid blasts (remember: the first diagonal is 1 space, the second is two, etc. This is counting from the center for my figures): [code] n=3 n=5 n=7 XXX XXX XXX XXX XXXXX XXXXX XXX XXXXX XXXXXXX XXXXX XXXXXXX XXX XXXXXXX XXXXX XXX [/code] Taxi-cab space is also a possibility--this is a space where you cannot move diagonally, only horizontally or vertically. The following are circles in taxi-cab space: [code] n=3 n=5 n=7 X X X XXX XXX XXX X XXXXX XXXXX XXX XXXXXXX X XXXXX XXX X [/code] Either of these geometries are much more amenable to cone-shaped areas than 4E's geometry. I suspect that's part of why they left cones out of the system completely--they just don't make sense. A further alternative that stays within 4E's geometry but allows for slightly more control would be to allow the shape of a blast to cover the caster's square (without actually damaging the caster): [code] OXX XXX XXX OXX XXX XXX [/code] My opinion is that allowing these two options for the casting shape increases the flexibility of blasts, but only to a very slight degree. The main increase in power here comes from the right figure, in which the caster can hit five adjacent enemies. If you forbid this option, all of the other shapes (including the left variant above) only allow the caster to hit three adjacent enemies--all of the other enemies must be further away. [/QUOTE]

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