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地图学·GIS
12
engines
Mercator projection · conformal but area-inflating
Mercator projection · conformal but area-inflating
x=Rλ,y=R·ln(tan(π/4+φ/2)) · 保角 · 面积∝sec φ
y = R·ln(tan(π/4 + φ/2)) keeps angles true but stretches area toward the poles
Projection distortion · Tissot's indicatrix
Projection distortion · Tissot's indicatrix
Tissot指示线 · 圆→椭圆 · 面积/角度变形对比
Tiny circles on the globe become ellipses that expose a map's area & angle errors
UTM coordinates · zones, easting & northing
UTM coordinates · zones, easting & northing
60带各6° · 带号=floor((lon+180)/6)+1 · 东距/北距
60 six-degree zones, each a transverse Mercator giving metric easting/northing
GPS trilateration · fixing position from ranges
GPS trilateration · fixing position from ranges
≥3卫星距离圆/球相交 · 接收机位置
Each measured distance to a known beacon is a circle; the fix is where all three meet
Dead reckoning · position from heading, speed & time
Dead reckoning · position from heading, speed & time
起点累加 v·t·(cosθ,sinθ) · 航向矢量 · 当前位置
Start known; each leg adds (speed × time) in the heading direction — position is a vector sum
Great-circle bearing · the initial heading of the shortest route
Great-circle bearing · the initial heading of the shortest route
θ=atan2(sinΔλcosφ2,cosφ1 sinφ2−sinφ1 cosφ2 cosΔλ)
θ = atan2( sinΔλ·cosφ₂ , cosφ₁·sinφ₂ − sinφ₁·cosφ₂·cosΔλ ) — degrees clockwise from north
Voronoi diagram · nearest-site partition
Voronoi diagram · nearest-site partition
最近站点划分平面为胞 · 垂直平分线边界
Each cell = the region of the plane closer to its site than to any other
Delaunay triangulation · empty circumcircle
Delaunay triangulation · empty circumcircle
Voronoi对偶 · 空外接圆性质 · 最大化最小角
No point lies inside any triangle's circumcircle — the dual of the Voronoi diagram
Contour interpolation · IDW & marching squares
Contour interpolation · IDW & marching squares
IDW反距离权/双线性 · marching squares 等值线
Reconstruct a surface from sampled heights, then trace iso-value contour lines
Slope & aspect from a DEM
Slope & aspect from a DEM
3×3窗口 dz/dx,dz/dy · slope=atan√ · aspect朝向
Horn 3×3 gradients · slope = atan(√(∂z/∂x² + ∂z/∂y²)) · aspect = atan2(−∂z/∂x, −∂z/∂y)
Map scale — fraction, words & bar
Map scale — fraction, words & bar
代表分数1:N · 地面=图上×N · 大/小比例尺
1:N ⇒ ground = map × N · ground_cm = map_cm × N
Datum transformation — same coordinate, different ground
Datum transformation — same coordinate, different ground
WGS84 vs 局部基准 · datum平移/Helmert · 地面位移
Δlat° = Δnorth/111320 · Δlon° = Δeast/(111320·cos φ) · shift = √(Δe²+Δn²)