3-D Surface Plotter
Z = f(X, Y) from your samples: rotatable surface, contour map and regressions.
Turns a table of samples into a three-dimensional response surface of one property against two others, as in published laboratory studies: classed colour surface with grid lines and a projected map on its base, a contour map with the samples, simple and multiple regression equations with R², and a written interpretation.
Overview
Paste the laboratory table (for example Atterberg limits, specific gravity, swelling indices and XRD mineral percentages), choose the two predictors and the response, and the tool fits the surface by thin-plate spline, distance-weighted least squares, inverse distance weighting or polynomial regression. The surface can be rotated through 360° and exported with its legend and equations.
What you enter · What you get
What you enter
- Table of samples with at least three numeric columns
- Choice of X, Y and Z
- Fitting method, smoothing and colour classes
What you get
- Rotatable 3-D surface with classed colours and projected base map
- Contour map with the samples
- Simple and multiple regression equations, R², adjusted R², cross-validation error
- PNG, JPG and PDF figures, CSV
How it works in the field
Method and equations
Surface fitting
Coordinates are scaled to 0–1 before fitting so that variables with different units weigh equally. The thin-plate spline minimises bending energy with an optional smoothing term; DWLS fits a local plane with Gaussian distance weights; IDW averages the samples with inverse-distance weights; the regressions fit a plane or a quadratic surface by least squares.
Statistics
Simple regressions of Z on X and on Y, multiple regression on both with adjusted R², the correlation between the two predictors to detect collinearity, and leave-one-out cross-validation of the fitted surface.
Accuracy and error limits
- The fitted surface passes through or near the samples; its leave-one-out cross-validation error, shown with the result, is the realistic error between samples. Regression R² describes fit, not predictive accuracy.
- Outside the range of the samples the surface is extrapolated; correlated predictors make regression coefficients unstable.
- To reduce the error: design the samples to cover the whole range of both variables, add replicates to estimate test scatter, and compare the surface with physical expectations.
Who uses it
Standards and references
- Duchon, J. (1977). Splines minimizing rotation-invariant semi-norms in Sobolev spaces. Lecture Notes in Mathematics, 571, 85–100.
- McLain, D.H. (1974). Drawing contours from arbitrary data points. The Computer Journal, 17(4), 318–324.
- Shepard, D. (1968). A two-dimensional interpolation function for irregularly-spaced data. Proc. 23rd ACM National Conference, 517–524.
- Fondjo, A.A. & Theron, E. (2020). Assessment of the mineral composition of heaving soils using geotechnical properties. Civil Engineering and Architecture, 8(4), 619–631.
At a glance
- Category
- Engineering & geotechnics
- Runs on
- Phone, tablet and desktop browser
- Export
- PNG, JPG and PDF figures, CSV, PDF report
- Access
- Subscribers
Run this survey on your next site
All 64 tools, report export and the AI assistant come with one subscription.