Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - .

Earthworks Volume Computation AlgorithmCASLE Jamaica Regional and International Conference 10/10/12

H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - [email protected]

A Robust Algorithmfor Earthworks

Volume Computations

Hakeeb A. Nandalal, BSc.Trinidad & Tobago Land Surveyor

http://[email protected]



OVERVIEW:

Objectives Requirements Methodology The Algorithm



OBJECTIVES

To obtain the Volume between Two Surfaces,Surface1 and Surface2

If Surface1 is 100% Above Surface2,this will be a “Cut” Volume Only

If Surface1 is 100% Below Surface2,this will be a “Fill” Volume Only

If Surface1 Intersects Surface2,there will be both a “Cut” Volume and a “Fill” Volume



Surface1

Surface2

Surface1 Above Surface2: Cut Volume Only



Surface1

Surface2

Surface1 Below Surface2: Fill Volume Only



Surface1

Surface2

Surface1 Intersects Surface2: Cut & Fill Volumes

Surface1



REQUIREMENTS

3D Data for Surface1 (Pre-Survey)

3D Data for Surface2 (Post-Survey)

A Method for Making Terrain Modelsfrom the 3D Data

An Algorithm for Comparing theTerrain Models to Derive

Cut & Fill Volumes



OBTAINING THE 3D DATAMEASUREMENT METHODS:

1. Spot Heights with Total Stations/GPS

2. Ground-Based LIDAR*

3. Aerial Survey: Photography/LIDAR

*LIDAR : Light Detection and Ranging



OBTAINING THE 3D DATA

Total Stations/GPS

Ground-Based LIDAR

Aerial Survey

GateWing X100



Surface1 XYZ Data Surface2 XYZ Data



Surface1 3D Points Plotted (Plan View)



Surface1 3D Points Plotted (Side View)

20m

0m



A METHOD FOR MAKING TERRAIN MODELSFROM THE 3D DATA

Delaunay Triangulation

In Mathematics and Computational Geometry,a Delaunay Triangulation for a Set of Pointsin a Plane, is a Triangulation such thatno other point in the Set is Inside the Circumcircleof a given Triangle.

The method is named after Boris Delaunayfor his work on this topic from 1934.



Delaunay Triangulation of Surface1

This is a 2D Operation using only the X,YValues of the 3D Points



Satisfying the Delaunay Triangulation Condition

Circumcircle



The Triangulation AlgorithmDescribed in Pseudo-Code:

subroutine triangulateinput : vertex listoutput : triangle list initialize the triangle list determine the supertriangle add supertriangle vertices to the end of the vertex list add the supertriangle to the triangle list for each sample point in the vertex list initialize the edge buffer for each triangle currently in the triangle list calculate the triangle circumcircle center and radius if the point lies in the triangle circumcircle then add the three triangle edges to the edge buffer remove the triangle from the triangle list endif endfor delete all doubly specified edges from the edge buffer this leaves the edges of the enclosing polygon only add to the triangle list all triangles formed between the point and the edges of the enclosing polygon endfor remove any triangles from the triangle list that use the supertriangle vertices remove the supertriangle vertices from the vertex listend

Source: http://paulbourke.net/papers/triangulate



OBTAINING VOLUMESFROM TERRAIN MODELS:

1. Between a Model and a Datum Plane

2. Between Two Models



Volume Computation between a 3D Triangle and a Plane

Triangle Above Plane




Triangle Below Plane




Triangle Intersecting Plane



Apply the Simple Computation toAll the 3D Triangles in the Model

Above

Below

Intersecting

Note: Slide #21

Datum Plane



Surface1

Surface2

Volume between Two Models



Plan View of Two Overlapping Models



A Detailed View of the Overlap

Surface1

Surface2

Overlapping Shapes Can be Triangles, Quadrilaterals, Pentagons & Hexagons



Typical Ways Two Triangles Can Overlap

All Overlap Shapes Can be Subdivided into Triangles



THE COMPOSITE METHOD FOR OBTAINING THEVOLUME BETWEEN TWO SURFACES:

Identify the Overlapping Areas

Deconstruct the Complex Shapes (Quadrilaterals,Pentagons & Hexagons) into Triangles

Create a “Height Difference”or Isopach Triangulated Surface

Use the Simple Computation for Obtaining theCut/Fill Volumes between the Isopach Surface

and the Zero Plane



Obtaining Z-Values of the Isopach Triangle

Vertically Non-Intersecting Planes



When Planes Collide

Vertically Intersecting Planes



The Two Surfaces The Isopach Surface



Apply the Simple Computation toAll the 3D Triangles in the Model

Above

Below

Intersecting

Zero Plane

(Recall Slide #21)

The IsopachSurface



Surface-To-Surface Volume Report

Surface1 Area = 10130.0 sq. mSurface2 Area = 10729.7 sq. mOverlapping Area = 10029.4 sq. mUnaffected Area = 0.0 sq. m

Area of Cut = 4879.8 sq. mArea of Fill = 5149.6 sq. mModified Area = 10029.4 sq. m

Max Z = 33.5 mMin Z = 14.2 mZ Range = 19.3 m

Cut Volume = 22198.39 Cubic MetresFill Volume = 17509.36 Cubic Metres

VOLUME REPORT USING THE COMPOSITE METHOD ON THETWO SURFACES USED IN THIS PRESENTATION(Windows Application Written in C by H. Nandalal)



SURFACE TO SURFACE VOLUME REPORT

Trimble5475 Kellenburger RoadDayton, Ohio 45424-1099, USA1-937-233-8921

Project: C:\Temp\tm.proReport Generated: Friday, October 05, 2012 11:34:07 PM--------------------------------------------------------------------------------Where the second surface is above the first the volume is reported as fill.Where the second surface is below the first the volume is reported asexcavation.--------------------------------------------------------------------------------

Shrinkage/swell factors: Excavation 1.0000 Fill 1.0000

First Surface Number Second Surface NumberLayer Name of Points Layer Name of Points--------------------------- ----------- ------------------------- ----------SURFACE-1 121 SURFACE-2 121

Excavation Volume (Cu. m.) Fill Volume (Cu. m.)-------------------------------- ---------------------------- 22,198.39 17,509.36

Net Difference: 4,689.04 Cu. m. Waste

VOLUME REPORT USING THE COMPOSITE METHOD ON THETWO SURFACES USED IN THIS PRESENTATION

(Application: TerraModel)



I would like to thank:

The Aubrey Barker Fund,Dr. Charisse Griffith-Charles

&CASLE Atlantic Region

for allowing me the opportunity topresent this paper.

Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - .

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