7afaa7db-aecb-4206-8b79-95a5a0ef9e73 23 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

The X, Y directions are strictly in ascending order, in literature: "metrics, knots, control points".

bilinear(x,y,M) ... Smath InterpBilinear(#,#,#,#,#)is obsolete x y M bilinear A M 112 M cols submatrix : B M 2 M rows 11 submatrix : C M 2 M rows 2 M cols submatrix : j 1 A length 2 range CC j el B C 1 C rows j j submatrix y linterp : for A transpose CC x linterp 51 line :

bilinear (x,y,M) . . .

Shall be linterp ... equivalent Quadratic

Smath code is like others => Universal.

Surface plot does not save settings.

surface(x,y):=bilinear(x,y,data)

Watch extrapolation ! ?

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Original data table data 0.3 0.45 0.6 0.6 0.4 0.5 - 0.62 - 0.65 0.4 0.48 - 0.6 - 0.61 0.38 0.45 0.55 0.59 44 mat :

Y 142 range : X 041 range transpose : data X Y data augment stack : data 11 el x/y : 41 line

data x/y 12341 0.3 0.45 0.6 0.6 2 0.4 0.5 - 0.62 - 0.65 3 0.4 0.48 - 0.6 - 0.61 4 0.38 0.45 0.55 0.59 55 mat

sanity check 00 data bilinear 0.5 0.5 data bilinear 32 data bilinear 23 data bilinear 2.5 3.5 data bilinear 51 mat 1 - 0.0875 - 0.62 - 0.48 - 0.02 - 51 mat

x y surface x y data bilinear :

surface

Explore an hypersurface

c 1 :

λ 1.5 :

f 2 c * y * 3 x 2^* y 2^* y 4^- c 2^x 2^y 2^+ (* - 4 c 4^* + (* x cos * y sinh * 2 c * y * x 4^3 y 2^* x 2^* - c 2^x 2^y 2^+ (* - 4 c 4^* - (* x sin * y cosh * x y * x 2^y 2^+ (y 2^x 2^- 2 c 2^* + (* (* 2 c * sin * 31 mat :

x y f f 1 el f 2 el + f 3 el + :

Interpolate this Hypersurface

A matrix may be from source [Engineering ...] or you can create from an f(x,y). The matrix from f(x,y) is essentially created from the "for-loop-counter". It can be square or rectangular in either direction X, Y ... bilinear(x,y,M) copes with either size [square/rectangular] ... here is the "for-loop-counter".

Mesh U, V  within the bounds L, H L H N xd U 0 : dx H L - N / : i 1 N 1 + (range U i el L dx i * dx - (+ : for U 41 line :

We make it symmetric by equating both directions. You may range V otherwise for an asymmetric option

L λ - : H λ : mesh 16 : 13 mat U L H mesh xd : V U : 12 mat M Min Max Scale Max Min - (M M min - M max M min - / (* Min + : 31 line

Generate the symmetric square hypersurface matrix x y f U V Sym r 1 : i 1 U rows range c 1 : j 1 V rows range M r c el U i el V j el f eval : c c 1 + : 21 line for r r 1 + : 31 line for M 31 line :

N x y f U V Sym :

Optimiz: numeric N N 0255 Scale :

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 N

N N 1 round vectorize :

New x/y U transpose augment U N augment stack :

New x/y 1.5 - 1.3125 - 1.125 - 0.9375 - 0.75 - 0.5625 - 1.5 - 0 51.8 83.1 101.5 111.9 117.5 1.3125 - 26.7 66.7 90.7 104.7 112.8 117.4 1.125 - 49 80.2 98.2 108.5 114.4 117.9 0.9375 - 66.2 91.5 105.2 112.5 116.5 118.8 0.75 - 78.2 100.3 111.2 116.4 118.8 120.1 0.5625 - 85.6 106.7 116.2 119.9 121.2 121.5 77 mat

sanity check 1.125 - 0.75 - New bilinear 0.75 - 1.125 - New bilinear 1.4 - 1.4 - New bilinear 31 mat 111.2 114.4 38.51 31 mat

x y M Spline A M 112 M cols submatrix : B M 2 M rows 11 submatrix : C M 2 M rows 2 M cols submatrix : j 1 A length 2 range CC j el B C 1 C rows j j submatrix y linterp : for A transpose CC x linterp 51 line :

Altitude x/y 02003000125 139.8 119.8 10 124.8 135.5 12050 114.4 139.2 122.3 120 121.1 137.7 121.1 190 123.2 135 123.3 64 mat :

200120 Altitude Spline 050 Altitude Spline 25085 Altitude Spline 31 mat 137.7 114.4 130.075 31 mat