Overview
I wanted the fitness challenge to show where you actually are on the journey. The map image has its own coordinate system and the route is a polyline with many segments. The only inputs we assume are: 1.) the total journey distance is 1779 miles, and 2.) the distance from Hobbiton to Bree is 120 miles.
我想在健身挑戰中準確顯示使用者在旅程中的位置。地圖影像有自己的座標系，路線是由許多線段組成的折線。 我們只假設兩個輸入：1)總旅程為 1779 英里 2.) 從霍比屯到布里為 120 英里。
Convert miles to map units
By sampling the Hobbiton to Bree segment we find that 1 mile ≈ 0.62259 map units (for this image/route). A quick sanity check—placing a test user at 120 miles lands them in Bree.
透過取樣霍比屯到布里的路段，我們得到 1 英里 ≈ 0.62259 地圖單位。將測試用戶設為 120 英里時， 會落在布里，驗證無誤。
Which segment am I on?
Let d be the user’s total distance traveled (in miles). Convert to map units with
dUnits = d × 0.62259. Walk the route’s segments, accumulating their lengths in map units until
the cumulative length exceeds dUnits—that segment is the one the user is on.
設使用者總里程為 d 英里，轉換為地圖單位 dUnits = d × 0.62259。依序累加各段長度，
當累積長度超過 dUnits 時，該段即為使用者所在的線段。
Place the point with trig
With the segment’s start (x₁,y₁) and end (x₂,y₂), compute
θ = atan2(y₂−y₁, x₂−x₁). The user’s offset along that segment is
t = (dUnits − cumulativeBefore) / segmentLength. Then:
ux = x₁ + t · (x₂ − x₁)
uy = y₁ + t · (y₂ − y₁)
You can also think of it using Euler / unit-vector components with cos θ and sin θ.
A refresher: Euler’s formula.
已知線段起點 (x₁,y₁) 與終點 (x₂,y₂)，先算
θ = atan2(y₂−y₁, x₂−x₁)。使用者在該段上的比例
t = (dUnits − 累積長度) / 該段長度，則
(ux, uy) 如上式。也可用單位向量
(cos θ, sin θ) 的觀點理解。