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## FULL SPECIFICATION# TACTICAL DICE GAME SYSTEM (TDGS) - CORE
# Title: Area of Effect
# Document: 16
# Version: 1.0
# Purpose: AI-readable specification for AoE shapes, distances, and targeting
# Target: Language models, AI assistants, game designers, developers
# License: MIT

================================================================================
CORE PRINCIPLE
================================================================================

AoE affects area, not entities. All entities in the area are affected.
No discrimination. Content can add smart targeting as ability trait.

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NOTATION
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FORMAT:
  [Shape][Primary][Direction][wWidth][hHeight]

SHAPE CODES:
  Code | Shape     | Direction Required?
  -----|-----------|--------------------
  Cir  | Circle    | No
  Con  | Cone      | Yes
  Lin  | Line      | Yes
  Rec  | Rectangle | No

DIRECTION CODES: N, NE, E, SE, S, SW, W, NW

DIRECTIONS ARE RELATIVE TO ENTITY:
  N = forward
  S = behind
  E = right
  W = left

NOTATION EXAMPLES:
  Notation   | Meaning
  -----------|----------------------------------
  Cir3       | Circle, radius 3
  Con4N      | Cone, length 4, forward
  Con4NE     | Cone, length 4, forward-right (diagonal)
  Lin5E      | Line, length 5, right
  Lin5Sw2    | Line, length 5, south, width 2
  Rec3x4     | Rectangle, 3 wide × 4 long
  Cir3h1     | Circle, radius 3, height 1
  Con6Nh10   | Cone, length 6, north, height 10

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DISTANCE
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CHEBYSHEV DISTANCE:
  Distance = max(|dx|, |dy|)

Diagonal = orthogonal. King's moves on chessboard.

BOUNDARIES: Always inclusive (≤ not <).

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SHAPES SUMMARY
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Shape              | Origin Affected | Total Squares  | Placement
-------------------|-----------------|----------------|------------
Circle             | Yes             | (2R+1)²        | At range
Cone (Cardinal)    | No              | L²             | From caster
Cone (Diagonal)    | No              | L(L+1)/2       | From caster
Line               | No              | L × W          | From caster
Rectangle          | Yes             | W × L          | At range

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CIRCLE
================================================================================

NOTATION: Cir[radius]

FORMULA: All squares where max(|dx|, |dy|) ≤ R from center

TOTAL: (2R+1)²

  Radius | Dimensions | Squares
  -------|------------|--------
  1      | 3×3        | 9
  2      | 5×5        | 25
  3      | 7×7        | 49
  4      | 9×9        | 81
  5      | 11×11      | 121

ORIGIN: Center of circle. IS affected.

PLACEMENT: At range (caster chooses center within range).

================================================================================
CONE (CARDINAL: N, E, S, W)
================================================================================

NOTATION: Con[length][direction]

WIDTH AT DISTANCE N: 2N - 1

TOTAL: L²

  Distance | Width | Running Total
  ---------|-------|---------------
  1        | 1     | 1
  2        | 3     | 4
  3        | 5     | 9
  4        | 7     | 16
  5        | 9     | 25
  6        | 11    | 36

ORIGIN: Caster's square. NOT affected.

PLACEMENT: Projects from caster in chosen direction.

================================================================================
CONE (DIAGONAL: NE, SE, SW, NW)
================================================================================

NOTATION: Con[length][direction]

WIDTH AT DISTANCE N: N

TOTAL: L(L+1)/2

  Distance | Width | Running Total
  ---------|-------|---------------
  1        | 1     | 1
  2        | 2     | 3
  3        | 3     | 6
  4        | 4     | 10
  5        | 5     | 15
  6        | 6     | 21

ORIGIN: Caster's square. NOT affected.

TRADEOFF: ~60% area of cardinal, but 8 total directions available.

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CONE SIZE COMPARISON
================================================================================

  Length | Cardinal | Diagonal
  -------|----------|----------
  2      | 4        | 3
  3      | 9        | 6
  4      | 16       | 10
  5      | 25       | 15
  6      | 36       | 21

================================================================================
LINE
================================================================================

NOTATION: Lin[length][direction] or Lin[length][direction]w[width]

TOTAL: L × W (width defaults to 1)

ORIGIN: Caster's square. NOT affected.

WIDE LINES: Origin expands to match width, centered on caster.

DIAGONAL LINES: One square per unit of length along diagonal path.

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RECTANGLE
================================================================================

NOTATION: Rec[width]x[length]

  Width = horizontal (east-west)
  Length = vertical (north-south)

TOTAL: W × L

ORIGIN: Corner placed within range. IS affected.

PLACEMENT: At range (like circles). Caster chooses corner position.
Extends in positive W and L directions.

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HEIGHT
================================================================================

DEFAULT RULE: Height = primary dimension

  Shape     | Primary Dimension | Default Height
  ----------|-------------------|---------------
  Circle    | Radius            | Radius
  Cone      | Length            | Length
  Line      | Length            | Length
  Rectangle | Larger of W, L    | Larger of W, L

OVERRIDE: Add h[N] to notation (e.g., Cir3h1)

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RESOLUTION
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TIMING: AoE resolves immediately. No reactions before resolution.

STEPS:
  1. Determine origin point
  2. Map shape
  3. Identify all entities in area
  4. Determine cover (from origin to each entity)
  5. Apply effect to each entity

ROLLS:
  - Per entity, independently
  - Standard d20 resolution
  - Luck applies (Document 4)

COVER (per Document 14):
  Cover Type | Bonus   | Effect
  -----------|---------|------------------
  Partial    | +2 REF  | Harder to hit
  Half       | +4 REF  | Much harder to hit
  Full       | —       | Not affected

Cover determined from AoE origin to each entity.

MULTI-SQUARE ENTITIES: Any overlap = affected (once).

STACKING: Multiple AoE effects apply independently.

================================================================================
CONTENT GUIDANCE
================================================================================

ABILITY DEFINITION:
  Property        | Required       | Example
  ----------------|----------------|----------------------------
  Shape           | Yes            | Cir3, Con4N, Lin5Ew2, Rec4x3
  Range           | Yes            | 20 squares, Self, Touch
  Height          | If override    | h1, h10
  Effect          | Yes            | 3d6 fire damage
  Resolution      | Yes            | INT vs REF
  Smart Targeting | If applicable  | Allies excluded

SMART TARGETING TRAITS:
  Trait           | Effect
  ----------------|-------------------------------
  Allies Excluded | Does not affect caster's side
  Enemies Only    | Only affects hostiles
  Selective       | Caster chooses targets in area

Not default. Content adds as needed.

================================================================================
QUICK REFERENCE - FORMULAS
================================================================================

  Shape          | Total Squares
  ---------------|---------------
  Circle         | (2R+1)²
  Cone Cardinal  | L²
  Cone Diagonal  | L(L+1)/2
  Line           | L × W
  Rectangle      | W × L

================================================================================
QUICK REFERENCE - ORIGIN RULES
================================================================================

  Shape     | Origin  | Affected? | Placement
  ----------|---------|-----------|------------
  Circle    | Center  | Yes       | At range
  Cone      | Caster  | No        | From caster
  Line      | Caster  | No        | From caster
  Rectangle | Corner  | Yes       | At range

================================================================================
QUICK REFERENCE - CONE WIDTH
================================================================================

  Distance | Cardinal | Diagonal
  ---------|----------|----------
  1        | 1        | 1
  2        | 3        | 2
  3        | 5        | 3
  4        | 7        | 4
  5        | 9        | 5

================================================================================
CROSS-REFERENCES
================================================================================

Document 3: Resolution Mechanics
  - Standard d20 resolution
  - Success thresholds

Document 4: Luck
  - Luck rerolls apply to AoE

Document 14: Movement and Positioning
  - Cover rules
  - Multi-square entities

================================================================================
CORE STATUS
================================================================================

STATUS: Canonical
VERSION: 1.0

This is a CORE document. It establishes fundamental AoE mechanics.

================================================================================
CANONICAL URLS
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Human-readable: https://tacticaldice.com/docs/tdgs/aoe
AI-optimized:   https://tacticaldice.com/docs/tdgs/aoeforai

================================================================================
END OF DOCUMENT
================================================================================
## SHAPES SUMMARYShapeOrigin AffectedTotal SquaresPlacement
CircleYes(2R+1)²At range
Cone (Cardinal)NoL²From caster
Cone (Diagonal)NoL(L+1)/2From caster
LineNoL × WFrom caster
RectangleYesW × LAt range
## FORMULASShapeTotal Squares
Circle(2R+1)²
Cone CardinalL²
Cone DiagonalL(L+1)/2
LineL × W
RectangleW × L
## ORIGIN RULESShapeOriginAffected?Placement
CircleCenterYesAt range
ConeCasterNoFrom caster
LineCasterNoFrom caster
RectangleCornerYesAt range
## CONE WIDTH BY DISTANCEDistanceCardinalDiagonal
111
232
353
474
595
## HEIGHT DEFAULTSShapePrimary DimensionDefault Height
CircleRadiusRadius
ConeLengthLength
LineLengthLength
RectangleLarger of W, LLarger of W, L
## KEY RULESRuleValue
Distance Formulamax(|dx|, |dy|) - Chebyshev
BoundariesInclusive (≤ not <)
ResolutionPer entity, independently
Multi-Square EntitiesAny overlap = affected once
StackingMultiple AoE apply independently
Smart TargetingNot default, content adds as trait
View Human-Readable Version
Shape	Origin Affected	Total Squares	Placement
Circle	Yes	(2R+1)²	At range
Cone (Cardinal)	No	L²	From caster
Cone (Diagonal)	No	L(L+1)/2	From caster
Line	No	L × W	From caster
Rectangle	Yes	W × L	At range
Shape	Total Squares
Circle	(2R+1)²
Cone Cardinal	L²
Cone Diagonal	L(L+1)/2
Line	L × W
Rectangle	W × L
Shape	Origin	Affected?	Placement
Circle	Center	Yes	At range
Cone	Caster	No	From caster
Line	Caster	No	From caster
Rectangle	Corner	Yes	At range
Shape	Primary Dimension	Default Height
Circle	Radius	Radius
Cone	Length	Length
Line	Length	Length
Rectangle	Larger of W, L	Larger of W, L
Rule	Value
Distance Formula	max(\|dx\|, \|dy\|) - Chebyshev
Boundaries	Inclusive (≤ not <)
Resolution	Per entity, independently
Multi-Square Entities	Any overlap = affected once
Stacking	Multiple AoE apply independently
Smart Targeting	Not default, content adds as trait