Difference between revisions of "Template:Lit Radius"
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*3: target light level - defaults to 0.3, which is all you probably want | *3: target light level - defaults to 0.3, which is all you probably want | ||
===Examples=== | ===Examples=== | ||
| − | + | *[[standing lamp]]<code><nowiki>{{Lit Radius|12|{{#expr:217+217+208}}}}</nowiki></code> -> {{Lit Radius|12|{{#expr:217+217+208}}}} | |
| + | *[[glow pod]]<code><nowiki>{{Lit Radius|6|{{#expr:113+141+117}}}}</nowiki></code> -> {{Lit Radius|6|{{#expr:113+141+117}}}} | ||
| + | *[[agarilux]]<code><nowiki>{{Lit Radius|10|{{#expr:23+15+30}}}}</nowiki></code> -> {{Lit Radius|10|{{#expr:23+15+30}}}} | ||
Combine with <code>#expr round</code> to improve readability: <code><nowiki>{{#expr: {{Lit Radius|12|{{#expr:217+217+208}}}} round 2}}</nowiki></code> -> {{#expr: {{Lit Radius|12|{{#expr:217+217+208}}}} round 2}} | Combine with <code>#expr round</code> to improve readability: <code><nowiki>{{#expr: {{Lit Radius|12|{{#expr:217+217+208}}}} round 2}}</nowiki></code> -> {{#expr: {{Lit Radius|12|{{#expr:217+217+208}}}} round 2}} | ||
===Maths=== | ===Maths=== | ||
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</pre> | </pre> | ||
This template substitutes (f) into the cubic equation and solves it using [https://quarticequations.com/Cubic.pdf Cardano's algorithm]. | This template substitutes (f) into the cubic equation and solves it using [https://quarticequations.com/Cubic.pdf Cardano's algorithm]. | ||
| + | [[Category: Math templates]] | ||
</noinclude><includeonly><!-- | </noinclude><includeonly><!-- | ||
-->{{#vardefine:glow_radius|{{{1|12}}}}}<!-- | -->{{#vardefine:glow_radius|{{{1|12}}}}}<!-- | ||
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-->{{#vardefine:a0|{{#expr:0 - {{#var:glow_radius}}*2/3}}}}<!-- | -->{{#vardefine:a0|{{#expr:0 - {{#var:glow_radius}}*2/3}}}}<!-- | ||
-->{{#vardefine:a2|{{#expr:{{#var:glow_radius}}*({{#var:f}}*5/3 - 1)}}}}<!-- | -->{{#vardefine:a2|{{#expr:{{#var:glow_radius}}*({{#var:f}}*5/3 - 1)}}}}<!-- | ||
| − | cardano | + | cardano-viete (a1 = 0) |
-->{{#vardefine:q|{{#expr:0 - {{#var:a2}}^2/9}}}}<!-- | -->{{#vardefine:q|{{#expr:0 - {{#var:a2}}^2/9}}}}<!-- | ||
-->{{#vardefine:r|{{#expr:0 - {{#var:a0}}/2 - {{#var:a2}}^3/27}}}}<!-- | -->{{#vardefine:r|{{#expr:0 - {{#var:a0}}/2 - {{#var:a2}}^3/27}}}}<!-- | ||
| − | -->{{#vardefine:u|{{#expr:({{#var:r}} + ({{#var:r}}^2 + {{#var:q}}^3)^(1/2))^(1/3)}}}}<!-- | + | -->{{#ifexpr:{{#var:r}}^2 + {{#var:q}}^3 > 0|<!-- cardano |
| − | -->{{#vardefine:v|{{#expr:({{#var:r}} - ({{#var:r}}^2 + {{#var:q}}^3)^(1/2))^(1/3)}}}}<!-- | + | ---->{{#vardefine:u|{{#expr:({{#var:r}} + ({{#var:r}}^2 + {{#var:q}}^3)^(1/2))^(1/3)}}}}<!-- |
| − | -->{{#vardefine:z1|{{#expr:{{#var:u}} + {{#var:v}} - {{#var:a2}}/3}}}}<!-- | + | ---->{{#vardefine:v|{{#expr:({{#var:r}} - ({{#var:r}}^2 + {{#var:q}}^3)^(1/2))^(1/3)}}}}<!-- |
| + | ---->{{#vardefine:z1|{{#expr:{{#var:u}} + {{#var:v}} - {{#var:a2}}/3}}}}<!-- | ||
| + | -->|<!-- viete | ||
| + | ---->{{#vardefine:theta|{{#expr:acos ({{#var:r}}/(0 - {{#var:q}})^(3/2))}}}}<!-- | ||
| + | ---->{{#vardefine:theta1|{{#expr:{{#var:theta}}/3}}}}<!-- | ||
| + | ---->{{#vardefine:z1|{{#expr:2 * (0 - {{#var:q}})^(1/2)*{{#expr:cos {{#var:theta1}}}} - {{#var:a2}}/3}}}}<!-- | ||
| + | -->}}<!-- | ||
-->{{#expr:{{#var:z1}} - 1}} | -->{{#expr:{{#var:z1}} - 1}} | ||
</includeonly> | </includeonly> | ||
Latest revision as of 13:08, 26 March 2023
Calculates the max distance of tiles away from a light source that tiles can be before they fall below 30% light (lit). This value rounded down is the last tile in a straight line that will count as lit - this distance doesn't include the light source's tile itself.
Parameters[edit]
- 1: glowRadius of the light source (e.g. 12 for standing lamp)
- 2: sum of the glowColor (e.g. 217+217+208 for standing lamp)
- 3: target light level - defaults to 0.3, which is all you probably want
Examples[edit]
- standing lamp
{{Lit Radius|12|{{#expr:217+217+208}}}}-> 9.092558072384
- glow pod
{{Lit Radius|6|{{#expr:113+141+117}}}}-> 3.4808904283651
- agarilux
{{Lit Radius|10|{{#expr:23+15+30}}}}-> 0.0029188183233999
Combine with #expr round to improve readability: {{#expr: {{Lit Radius|12|{{#expr:217+217+208}}}} round 2}} -> 9.09
Maths[edit]
The light value (glow) a certain distance away from a light source is determined as a combination of a linear decay based on distance relative to glowRadius (a), and the inverse of the distance squared (b). These two numbers are combined with 60% from (a) and 40% from (b) to give a multiplier (f) to the sum of the glowColors, which then directly determines the light value at the tile.
r = glowRadius d = distance + 1 c = sum(glowColors) a = 1 - d/r b = 1/(d*d) f = a + (b-a)*0.4 glow = max(0, min(0.5, f*c/3/255*3.6))
The middle equations can be rearranged into a cubic equation in (d) in terms of (r) and (f), and the bottom equation can be rearranged for (f) in terms of (c) and (glow), provided 0 < (glow) < 0.5:
0 = -r*2/3 + r*(f*5/3 - 1)*d^2 + d^3 f = glow/c*3*255/3.6
This template substitutes (f) into the cubic equation and solves it using Cardano's algorithm.