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Areas of effect in 3 dimensions
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<blockquote data-quote="Tenniel" data-source="post: 4403824" data-attributes="member: 61866"><p>There are rules for adjudicating 3D action. DMG p45 says (and I'm paraphrasing) when measuring to an elevated target you take the maximum of:</p><p>1) difference in height and</p><p>2) distance as measured on the horizontal plane (i.e. number of squares away on the battle mat) .</p><p> </p><p>*If* you apply this distance measuring to areas *then* blasts are cubes.</p><p> </p><p>If firecubes offend you, you can house-rule blasts and bursts are sphere or cones or whatever.</p><p> </p><p>In 3e I generated 3D templates for area effects using the rules in the manuals. Problem was with players. They complained my templates did not agree with the official RPGA templates they had. Also the templates offered as guidelines in the 3.5 manuals did not agree with the ones I generated. I got tired of arguing my case, so I retired them. At ground zero, a fireball looked like</p><p> </p><p><span style="font-family: 'Courier New'">..xxxx..</span></p><p><span style="font-family: 'Courier New'">.xxxxxx.</span></p><p><span style="font-family: 'Courier New'">xxxxxxxx</span></p><p><span style="font-family: 'Courier New'">xxxxxxxx</span></p><p><span style="font-family: 'Courier New'">xxxxxxxx</span></p><p><span style="font-family: 'Courier New'">xxxxxxxx</span></p><p><span style="font-family: 'Courier New'">.xxxxxx.</span></p><p><span style="font-family: 'Courier New'">..xxxx..</span></p><p> </p><p>You can make these easily using a "monte carlo simulation" to determine if a square has more than 50% of its volume in the area of effect. Using the results yiou can generate a template for "ground zero- 5ft. altitude", "5ft. altitude-10 ft. altitude ", "10ft. altitude-15 ft. altitude " and so on. Essentianlly, 5 ft. thick horizontal slices through the fireball.</p><p> </p><p>But (wah!) I have lost my code. But it is really simple you generate random (hence "mote carlo", you see... quite an approriate numerical method RPGers?) points in every 5x5x5 cube, check to see if each pont falls within the sphere (using good ol' Pythagoras' theorem) and after generating many of these work out what propotion fell within the sphere. If more than 50%, then the cube is in the area of effect. Easy peasy.</p><p> </p><p>Here are the proportions of points at ground zero - 5ft. for a 20 ft. radius:</p><p><span style="font-family: 'SAS Monospace'"><span style="font-size: 9px"><span style="font-family: 'SAS Monospace'"><span style="font-size: 9px">0.000‚0.126‚<span style="color: red">0.646‚0.911‚0.915‚0.647</span>‚0.127‚0.000‚</span></span></span></span></p><p><span style="font-family: 'SAS Monospace'"><span style="font-size: 9px"><span style="font-size: 9px"><span style="font-family: 'SAS Monospace'"><span style="color: red"><span style="color: white">0.132</span>‚0.917‚1.000‚1.000‚1.000‚1.000‚0.915‚</span><span style="color: white">0.128</span></span></span></span></span></p><p><span style="font-family: 'SAS Monospace'"><span style="font-size: 9px"><span style="font-size: 9px"><span style="font-family: 'SAS Monospace'"><span style="color: red">0.646‚1.000‚1.000‚1.000‚1.000‚1.000‚1.000‚0.652</span></span></span></span></span></p><p><span style="font-family: 'SAS Monospace'"><span style="font-size: 9px"><span style="font-size: 9px"><span style="font-family: 'SAS Monospace'"><span style="color: red">0.911‚1.000‚1.000‚1.000‚1.000‚1.000‚1.000‚0.914</span></span></span></span></span></p><p><span style="font-family: 'SAS Monospace'"><span style="font-size: 9px"><span style="font-size: 9px"><span style="font-family: 'SAS Monospace'"><span style="color: red">0.915‚1.000‚1.000‚1.000‚1.000‚1.000‚1.000‚0.916</span></span></span></span></span></p><p><span style="font-family: 'SAS Monospace'"><span style="font-size: 9px"><span style="font-size: 9px"><span style="font-family: 'SAS Monospace'"><span style="color: red">0.651‚1.000‚1.000‚1.000‚1.000‚1.000‚1.000‚0.639</span></span></span></span></span></p><p><span style="font-family: 'SAS Monospace'"><span style="font-size: 9px"><span style="font-size: 9px"><span style="font-family: 'SAS Monospace'">0.131‚<span style="color: red">0.912‚1.000‚1.000‚1.000‚1.000‚0.918</span>‚0.129</span></span></span></span></p><p><span style="font-family: 'SAS Monospace'"><span style="font-size: 9px"><span style="font-size: 9px"><span style="font-family: 'SAS Monospace'">0.000‚0.128‚<span style="color: red">0.647‚0.918‚0.912‚0.649</span>‚0.128‚0.000</span></span></span></span></p><p><span style="font-family: 'SAS Monospace'"><span style="font-size: 9px"></span></span></p><p>So the 3.5e DMG template guideline did not precisely follow the text descrption</p></blockquote><p></p>
[QUOTE="Tenniel, post: 4403824, member: 61866"] There are rules for adjudicating 3D action. DMG p45 says (and I'm paraphrasing) when measuring to an elevated target you take the maximum of: 1) difference in height and 2) distance as measured on the horizontal plane (i.e. number of squares away on the battle mat) . *If* you apply this distance measuring to areas *then* blasts are cubes. If firecubes offend you, you can house-rule blasts and bursts are sphere or cones or whatever. In 3e I generated 3D templates for area effects using the rules in the manuals. Problem was with players. They complained my templates did not agree with the official RPGA templates they had. Also the templates offered as guidelines in the 3.5 manuals did not agree with the ones I generated. I got tired of arguing my case, so I retired them. At ground zero, a fireball looked like [FONT=Courier New]..xxxx..[/FONT] [FONT=Courier New].xxxxxx.[/FONT] [FONT=Courier New]xxxxxxxx[/FONT] [FONT=Courier New]xxxxxxxx[/FONT] [FONT=Courier New]xxxxxxxx[/FONT] [FONT=Courier New]xxxxxxxx[/FONT] [FONT=Courier New].xxxxxx.[/FONT] [FONT=Courier New]..xxxx..[/FONT] You can make these easily using a "monte carlo simulation" to determine if a square has more than 50% of its volume in the area of effect. Using the results yiou can generate a template for "ground zero- 5ft. altitude", "5ft. altitude-10 ft. altitude ", "10ft. altitude-15 ft. altitude " and so on. Essentianlly, 5 ft. thick horizontal slices through the fireball. But (wah!) I have lost my code. But it is really simple you generate random (hence "mote carlo", you see... quite an approriate numerical method RPGers?) points in every 5x5x5 cube, check to see if each pont falls within the sphere (using good ol' Pythagoras' theorem) and after generating many of these work out what propotion fell within the sphere. If more than 50%, then the cube is in the area of effect. Easy peasy. Here are the proportions of points at ground zero - 5ft. for a 20 ft. radius: [FONT=SAS Monospace][SIZE=1][FONT=SAS Monospace][SIZE=1]0.000‚0.126‚[COLOR=red]0.646‚0.911‚0.915‚0.647[/COLOR]‚0.127‚0.000‚[/SIZE][/FONT] [SIZE=1][FONT=SAS Monospace][COLOR=red][COLOR=white]0.132[/COLOR]‚0.917‚1.000‚1.000‚1.000‚1.000‚0.915‚[/COLOR][COLOR=white]0.128[/COLOR][/FONT][/SIZE] [SIZE=1][FONT=SAS Monospace][COLOR=red]0.646‚1.000‚1.000‚1.000‚1.000‚1.000‚1.000‚0.652[/COLOR][/FONT][/SIZE] [SIZE=1][FONT=SAS Monospace][COLOR=red]0.911‚1.000‚1.000‚1.000‚1.000‚1.000‚1.000‚0.914[/COLOR][/FONT][/SIZE] [SIZE=1][FONT=SAS Monospace][COLOR=red]0.915‚1.000‚1.000‚1.000‚1.000‚1.000‚1.000‚0.916[/COLOR][/FONT][/SIZE] [SIZE=1][FONT=SAS Monospace][COLOR=red]0.651‚1.000‚1.000‚1.000‚1.000‚1.000‚1.000‚0.639[/COLOR][/FONT][/SIZE] [SIZE=1][FONT=SAS Monospace]0.131‚[COLOR=red]0.912‚1.000‚1.000‚1.000‚1.000‚0.918[/COLOR]‚0.129[/FONT][/SIZE] [SIZE=1][FONT=SAS Monospace]0.000‚0.128‚[COLOR=red]0.647‚0.918‚0.912‚0.649[/COLOR]‚0.128‚0.000[/FONT][/SIZE] [/SIZE][/FONT] So the 3.5e DMG template guideline did not precisely follow the text descrption [/QUOTE]
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