Wall-Mounted Faucet Layout

Source: https://github.com/starsy/wall-mounted-faucet-layout-skill

intent

Use this skill when selecting a wall-mounted faucet or validating its installation geometry against a basin. the skill solves for one unknown dimension (reach L, outlet height H1, drain location WS, stream angle theta, wall setback K, or drain depth H2) given the other five, then validates the result geometrically and suggests an on-site water test before concealed installation. it's the standard reference for faucet specifiers, plumbers, and designers who need to reconcile faucet reach, basin rim height, drain position, and water flow angle in one coordinate system.

inputs

geometry parameters (provide 5 of 6; the skill solves for the 6th):

• K: finished wall to rear inner basin wall, in consistent unit (mm, cm, m)
• WS: rear inner basin wall to drain center, in same unit (or derive from W)
• W: front-to-back inner basin width; optional, used to calculate centered drain as WS = W / 2
• H1: basin rim to faucet outlet, vertical upward, in same unit
• H2: basin rim to drain target point, vertical downward, in same unit
• L: finished wall to faucet outlet, horizontal reach, in same unit
• theta: water flow angle from vertical, in degrees (0 to 90 typical; positive means forward away from wall)

setup and dependencies:

• calculator script: scripts/faucet_geometry.py (python 3.6+, no external deps)
• SVG renderer: scripts/render_geometry_svg.py (python 3.6+ with svg library)
• reference diagrams: assets/wall_mounted_faucet_geometry_v2.svg (english) or assets/wall_mounted_faucet_geometry_v2_zh.svg (chinese)
• no external APIs or auth required

edge cases and constraints:

• all lengths must use one unit throughout (no mixing cm and inches)
• theta must be 0 to 90 degrees for forward flow; theta exactly 0 or 90 will cause division errors
• if H1 < 0, the outlet sits below the basin rim (incompatible geometry)
• if K + WS - L < 0, the drain lies behind the faucet outlet (water cannot reach it)
• if WS is not supplied and W is unknown, the skill cannot resolve drain location and will halt

procedure

1. identify the target variable. ask the user which dimension they want to solve for, or infer from context: prefer L (faucet reach) if choosing a faucet model, or H1 (outlet height) if checking a candidate faucet against wall rough-in. do not assume the user wants H1 + H2 as a "recommended drop"; that is geometry-dependent.

2. collect five known dimensions from the user and confirm units. if WS is not provided and W is known, set WS = W / 2 and note that the drain is centered.

3. validate inputs:

   • all five known values must be finite and positive (or zero for offsets).
   • theta must be > 0 and < 90 degrees.
   • if W is known, check 0 < WS < W.

4. convert theta to radians: multiply degrees by pi / 180.

5. select and substitute into the target formula:

   • solve for H1: H1 = (K + WS - L) / tan(theta) - H2
   • solve for L: L = K + WS - (H1 + H2) * tan(theta)
   • solve for WS: WS = L - K + (H1 + H2) * tan(theta)
   • solve for theta: theta = arctan((K + WS - L) / (H1 + H2)), then convert result to degrees
   • solve for K: K = L - WS + (H1 + H2) * tan(theta)
   • solve for H2: H2 = (K + WS - L) / tan(theta) - H1

6. calculate: use scripts/faucet_geometry.py with the target variable and known inputs. do not perform trigonometry mentally.

7. run validation checks (see decision points and output contract below).

8. reverse-check: substitute the solved value back into tan(theta) = (K + WS - L) / (H1 + H2) and confirm the angle matches the input theta within 0.1 degrees.

9. generate visual output if requested: call scripts/render_geometry_svg.py with the same inputs and solved value to create an annotated SVG for client or installer handoff.

10. deliver the result in the response template below, including practical guidance and a recommendation for on-site water testing before concealed installation.

decision points

• if user asks for "the right faucet" and provides outlet height + basin geometry: solve for L first. the result is the faucet reach to buy.

• if user provides a faucet model number or reach L and wants to know if it fits the wall rough-in: solve for H1 first. compare the result against the available wall space.

• if WS is not supplied but W is known: assume the drain is centered at WS = W / 2. call this out in the response so the user can confirm or correct the drain position.

• if theta is outside 0 to 90 degrees or equals 0 or 90 exactly: halt and ask the user to clarify the flow angle. theta = 0 is straight down (faucet directly above drain, no horizontal reach needed). theta = 90 is horizontal (geometry breaks down mathematically).

• if K + WS - L < 0: the drain is behind the faucet outlet under this coordinate convention. the geometry is impossible. ask the user to verify K, WS, or L.

• if H1 < 0 after solving: the outlet would sit below the basin rim. ask whether the reference line (basin rim vs. basin floor) is correct, or whether the user wants a negative result (uncommon but valid in some deep-basin cases).

• if the user requests visual output: generate SVG with scripts/render_geometry_svg.py. write to a user-visible filename like faucet-layout-{project-name}.svg.

output contract

numeric result:

• formula text (e.g., "L = K + WS - (H1 + H2) * tan(theta)")
• substitution (e.g., "L = 5 + 20 - (15 + 14) * tan(10°)")
• exact floating-point result (e.g., "19.8890 cm")
• practical rounded result in user's unit (e.g., "19.9 cm", "20 mm", "0.200 m")
• all intermediate values (horizontal offset Δx, vertical drop Δy)

validation output:

• reverse-check angle (must match input theta within 0.1 degrees)
• drain offset from basin center if W is known: center_offset = WS - W / 2 (positive = forward, negative = rear, zero = centered)
• pass/fail for each validation rule

selection guidance:

• if solving L: "compare this reach against the faucet spec sheet projection from finished wall to outlet"
• if solving H1: "compare this outlet height against the available wall rough-in and desired clearance above the basin rim"

SVG output (when requested):

• file path and name (e.g., faucet-layout-kitchen.svg)
• dimensions and labels annotated directly in the diagram
• solved value highlighted
• practical warning note embedded in the visual

outcome signal

the skill worked if:

1. the numeric result and all validation checks pass, and the user can compare the result against a real faucet spec sheet or wall rough-in dimension.
2. the user confirms that the solved dimension makes sense (e.g., "yes, a 20 cm reach faucet is available" or "yes, 12 cm outlet height fits the wall").
3. if visual output was requested, the user receives a clear, annotated SVG diagram they can hand to a plumber or use for client review.
4. the user schedules an on-site water test or confirms the installation with a mock-up before concealing the faucet rough-in.

if the reverse-check fails (solved dimension plugged back in does not recover the input theta), report the discrepancy and halt. if validation rules reject the geometry, report which constraint failed and suggest correcting K, WS, L, or theta.

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reference: coordinate convention

All linear measurements use the same unit. Horizontal distance increases from the wall toward the front of the basin. Vertical distance increases downward from the faucet outlet toward the drain. Theta is measured from vertical; positive theta means water points forward, away from the wall.

Symbol	Meaning
K	Finished wall to rear inner basin wall
W	Front-to-back inner width of the basin
WS	Rear inner basin wall to drain center
L	Finished wall to faucet outlet
H1	Basin rim to faucet outlet, vertically upward
H2	Basin rim to drain target point, vertically downward
theta	Water angle from vertical, in degrees

If drain is centered: WS = W / 2.

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reference: core geometry

Horizontal offset: Δx = K + WS - L

Vertical drop: Δy = H1 + H2

Core relationship: tan(theta) = (K + WS - L) / (H1 + H2)

This models the water path as a straight centerline. Real water curves under gravity and varies with pressure, aerator design, and flow rate; always confirm with on-site testing.

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reference: sensitivity

For fixed K, WS, H2, and theta:

∂H1 / ∂L = -1 / tan(theta)

At theta = 10°: 1 / tan(10°) ≈ 5.67, so increasing L by 1 cm lowers theoretical H1 by about 5.67 cm.

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worked examples

Example 1: choose faucet reach, solve for L

Given K=5 cm, WS=20 cm, H1=15 cm, H2=14 cm, theta=10°:

L = 5 + 20 - (15 + 14) * tan(10°) ≈ 19.89 cm

Interpretation: choose a faucet whose outlet projects about 19.9 cm from the finished wall, then verify with real water flow.

Example 2: check mounting height, solve for H1

Given K=5 cm, W=40 cm, H2=14 cm, L=20.5 cm, theta=10° (so WS=20):

H1 = (5 + 20 - 20.5) / tan(10°) - 14 ≈ 11.52 cm

Interpretation: this faucet reach works geometrically if the outlet can sit about 11.5 cm above the basin rim.

Example 3: short reach, solve for H1

Given K=5 cm, WS=20 cm, H2=14 cm, L=16 cm, theta=10°:

H1 = (5 + 20 - 16) / tan(10°) - 14 ≈ 37.04 cm

The large result is expected because a 10-degree stream is close to vertical.

Example 4: secondary check, solve for WS

Given K=5 cm, H1=15 cm, H2=14 cm, L=20.5 cm, theta=10°:

WS = 20.5 - 5 + (15 + 14) * tan(10°) ≈ 20.61 cm

For W=40 cm, the drain is approximately 0.61 cm forward of center.

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command reference

calculate numeric result:

python scripts/faucet_geometry.py --solve L --K 5 --WS 20 --H1 15 --H2 14 --theta 10 --unit cm
python scripts/faucet_geometry.py --solve H1 --K 5 --W 40 --H2 14 --L 20.5 --theta 10 --unit cm

generate annotated SVG:

python scripts/render_geometry_svg.py --solve L --K 5 --WS 20 --H1 15 --H2 14 --theta 10 --unit cm --output faucet-layout.svg

The calculator defaults to practical precision (whole mm, 0.1 cm, 0.001 m, 0.1 degrees). Use --precision only if the user explicitly requests higher precision.

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implementation notes for agents

• Always use the provided scripts for calculation. do not estimate trig values mentally.
• Prefer deterministic, reproducible results with full floating-point precision internally, then display rounded to practical engineering precision.
• When the user asks for a visual explanation, diagram, client handoff, or installer handoff, generate SVG. write to a project-specific output path.
• recommend an on-site water test before concealing any rough-in. straight-line geometry does not account for water curve, aerator design, flow rate, or pressure loss.
• if the user provides incomplete geometry, ask clarifying questions instead of assuming missing values (except WS from W, which is a standard assumption).

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Original skill source: clawhub (github.com/starsy/wall-mounted-faucet-layout-skill). Procedure and formulas preserved from original.