MalcolmWoodruff/ LineTerra

Earthworks design and quantification toolkit

Contributed by: Malcolm Woodruff

LineTerra turns the Wolfram Language into an earthworks design and quantification workstation. Its core method threads a cross-section template along an alignment and calculates its intersection with the existing ground; a separate polygon tool handles footprint-based earthworks such as building pads. Although most worked examples design roads -- horizontal alignment with circular or Bezier intersection-point curves, vertical profile with K-value parabolic curves, and cross-section templates carrying carriageway links, cut and fill batters, ditches, walls and bridge or tunnel structures -- the same procedure applies to slope-stability cross-sections, dam design and reservoir volumes, drainage networks, and single-building pads. Output covers cut and fill quantities including a mass-haul diagram, 3D visualization, and export to CSV, true-scale PDF, PNG, DXF and native notebooks.

Installation Instructions

To install this paclet in your Wolfram Language environment, evaluate this code:
PacletInstall["MalcolmWoodruff/LineTerra"]


To load the code after installation, evaluate this code:
Needs["MalcolmWoodruff`LineTerra`"]

Details

Terrain can be read from a GeoTIFF raster, from Wolfram's own GeoElevationData, from a delimited XYZ survey file, from a compressed LAZ or uncompressed LAS LIDAR point cloud, or from a synthetic corridor strip.
Optional named geological strata are shown as coloured bands on each cross-section. This feature is in preparation.
Multiple roads, or other alignments, can share a single terrain. Every crossing between them can be found automatically, and a finished design's formation can be baked into the terrain so the next one is designed on top of it.
Quantities use average-end-area volumes between sections with an eccentric end-area correction for curvature, and can be no more accurate than the terrain data supplied.
The interface is built from Dynamic content, dialogs, palettes and CreateDocument windows, so LineTerra needs the notebook front end; it will not run under a bare kernel or wolframscript.
LAZ point-cloud terrain is the one feature that is not pure Wolfram Language: the Wolfram Language has no native LAZ decompressor, so LineTerra delegates to an external decoder -- PDAL, recommended, or the LASzip command-line tool -- and reads the resulting LAS file natively. Uncompressed.las files need no external tool. Everything else is pure Wolfram Language.
See additional details and notes about the paclet in the User Manual.

Examples

Basic Examples (4) 

Open the LineTerra toolbar for a project. This is the entry point to every other window -- Terrain, Plan/Profile, Intersect, Templates, Sections, Earthwork, Export, 3D View and Bake Road. Evaluating it again with the same name reopens that road; with a different name it opens another road on the same terrain:

In[1]:=
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Out[1]=

The alignment and profile geometry is plain kernel code. Cumulative chainage along a three-point alignment:

In[2]:=
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Out[2]=

Rounding the corner with a 40 m arc shortens the route from the 200 m walked by the two straight legs:

In[3]:=
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Out[3]=

The design level at a chainage, with a parabolic vertical curve applied at the crest. The grade changes from +10% to -5%, a change of 15%, so a K-value of 5 gives a 75 m vertical curve:

In[4]:=
InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 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Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["MalcolmWoodruff/LineTerra", "MalcolmWoodruff`LineTerra`LTDesignZCurved"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][{{0, 10}, {100, 20}, {200, 15}}, {0, 5, 0}, 100]
Out[4]=

Scope (6) 

Terrain comes from whichever source suits the stage of the project. A GeoTIFF elevation raster, with its.tfw world file or with the georeferencing tags embedded in the file itself:

In[5]:=
terrain = InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 307.0436840057373`], List[153.98200225830078`, 235.99870109558105`], List[195.`, 212.31669425964355`], List[195.`, 22.863691329956055`], List[30.928985595703125`, 117.59068870544434`], List[30.928985595703125`, 307.0436840057373`]], List[List[200.`, 410.42970085144043`], List[364.0710144042969`, 315.7036876678467`], List[241.01799774169922`, 244.65868949890137`], List[200.`, 220.97669792175293`], List[158.98200225830078`, 244.65868949890137`], List[35.928985595703125`, 315.7036876678467`], List[200.`, 410.42970085144043`]], List[List[376.5710144042969`, 320.03370475769043`], List[202.5`, 420.53370475769043`], List[200.95300006866455`, 421.42667961120605`], List[199.04699993133545`, 421.42667961120605`], List[197.5`, 420.53370475769043`], List[23.428985595703125`, 320.03370475769043`], List[21.882003784179688`, 319.1406993865967`], List[20.928985595703125`, 317.4896984100342`], List[20.928985595703125`, 315.7036876678467`], List[20.928985595703125`, 114.70369529724121`], 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Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["MalcolmWoodruff/LineTerra", "MalcolmWoodruff`LineTerra`LTLoadGeoTIFF"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]]["terrain.tif", "terrain.tfw"]

A LIDAR point cloud, gridded from its ground-classified points. A.laz file needs PDAL or LASzip on the system path; a.las file is read with no external tool:

In[6]:=
terrain = InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 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0]]], List[List[List[44.92900085449219`, 282.59088134765625`], List[181.00001525878906`, 204.0298843383789`], List[181.00001525878906`, 46.90887451171875`], List[44.92900085449219`, 125.46986389160156`], List[44.92900085449219`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6627450980392157`, 0.803921568627451`, 0.5686274509803921`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[355.0710144042969`, 282.59088134765625`], List[355.0710144042969`, 125.46986389160156`], List[219.`, 46.90887451171875`], List[219.`, 204.0298843383789`], List[355.0710144042969`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6901960784313725`, 0.5882352941176471`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[200.`, 394.0606994628906`], List[336.0710144042969`, 315.4997024536133`], List[200.`, 236.93968200683594`], 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Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["MalcolmWoodruff/LineTerra", "MalcolmWoodruff`LineTerra`LTLoadLAZTerrain"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]]["survey.laz", "GridSpacing" -> 2]

A synthetic corridor strip following the assumed route centreline, which keeps a very long route's terrain to a workable size. Make the number of cross samples odd, so one falls on the centreline:

In[7]:=
terrain = InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 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Work can be carried out in latitude and longitude or in a national grid, and most countries' grids are supported. Converting to the British National Grid:

In[8]:=
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Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["MalcolmWoodruff/LineTerra", "MalcolmWoodruff`LineTerra`LTConvertToGrid"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][50.65, -1.25, "OSGB36"]
Out[8]=

Any UTM zone or other supported projection can be named by its EPSG code directly:

In[9]:=
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Out[9]=

Cross-sections export to PDF at an exact drawing scale, to a notebook as named vector graphics, or to true-scale DXF. DXF coordinates are real-world metres -- one drawing unit is one metre -- with geometry separated onto per-section GROUND, DESIGN and SCALE layers:

In[10]:=
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Applications (11) 

First, evaluate the follwoing and you will get the main menu. Choose New Project then Terrain:

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Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["MalcolmWoodruff/LineTerra", "MalcolmWoodruff`LineTerra`LineTerra"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]]["Example 2 Road A"]
Out[11]=

Press LAZ/LAS point Cloud. If it is a LAZ file then you must have PDAL or LASzip on the system path, e. g.: brew install pdal. (See “Read this first). If you have or it is a LAS file the file will be read directly:

The preview can be shown in the normal way:

Pressing Plan and then adding IPs to form a road alignment:

Extracting a profile:

Either open a template library or design new ones. Here we have opened the library so we can use the motorway and bridge templates:

Assign sections to the alignment:

Calculating earthworks we get an updated plan:

And earthwork quantities:

Leaving Earthworks on Auto we can then adjust the profile and/or the planned alignment and the quantities and plan will instantly update:

The road can be baked into the terrain and a 3D image produced. Sections or the plan can be exported to scale:

Publisher

Malcolm Woodruff

Compatibility

Wolfram Language Version 13.0

Version History

  • 1.0.0 – 16 August 2026

License Information

MIT License

Paclet Source

See Also