1. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt A Robust Algorithm for Earthworks Volume Computations Hakeeb A. Nandalal, BSc. Trinidad & Tobago Land Surveyor http://www.survplan.com nanco@tstt.net.tt

2. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt OVERVIEW:  Objectives  Requirements  Methodology  The Algorithm

3. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt 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

4. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Surface1 Surface2 Surface1 Above Surface2: Cut Volume Only

5. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Surface1 Surface2 Surface1 Below Surface2: Fill Volume Only

6. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Surface1 Surface2 Surface1 Intersects Surface2: Cut & Fill Volumes Surface1

7. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt REQUIREMENTS 3D Data for Surface1 (Pre-Survey) 3D Data for Surface2 (Post-Survey) A Method for Making Terrain Models from the 3D Data An Algorithm for Comparing the Terrain Models to Derive Cut & Fill Volumes

8. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt OBTAINING THE 3D DATA MEASUREMENT METHODS: 1. Spot Heights with Total Stations/GPS 2. Ground-Based LIDAR* 3. Aerial Survey: Photography/LIDAR *LIDAR : Light Detection and Ranging

9. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt OBTAINING THE 3D DATA Total Stations/GPS Ground-Based LIDAR Aerial Survey GateWing X100

10. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Surface1 XYZ Data Surface2 XYZ Data

11. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Surface1 3D Points Plotted (Plan View)

12. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Surface1 3D Points Plotted (Side View) 20m 0m

13. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt A METHOD FOR MAKING TERRAIN MODELS FROM THE 3D DATA Delaunay Triangulation In Mathematics and Computational Geometry, a Delaunay Triangulation for a Set of Points in a Plane, is a Triangulation such that no other point in the Set is Inside the Circumcircle of a given Triangle. The method is named after Boris Delaunay for his work on this topic from 1934.

14. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Delaunay Triangulation of Surface1 This is a 2D Operation using only the X,Y Values of the 3D Points

15. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Satisfying the Delaunay Triangulation Condition Circumcircle

16. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt The Triangulation Algorithm Described in Pseudo-Code: subroutine triangulate input : vertex list output : 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 list end Source: http://paulbourke.net/papers/triangulate

17. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt OBTAINING VOLUMES FROM TERRAIN MODELS: 1. Between a Model and a Datum Plane 2. Between Two Models

18. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Volume Computation between a 3D Triangle and a Plane Triangle Above Plane

19. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Volume Computation between a 3D Triangle and a Plane Triangle Below Plane

20. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Volume Computation between a 3D Triangle and a Plane Triangle Intersecting Plane

21. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Apply the Simple Computation to All the 3D Triangles in the Model Above Below Intersecting Note: Slide #21 Datum Plane

22. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Surface1 Surface2 Volume between Two Models

23. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Plan View of Two Overlapping Models

24. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt A Detailed View of the Overlap Surface1 Surface2 Overlapping Shapes Can be Triangles, Quadrilaterals, Pentagons & Hexagons

25. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Typical Ways Two Triangles Can Overlap All Overlap Shapes Can be Subdivided into Triangles

26. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt THE COMPOSITE METHOD FOR OBTAINING THE VOLUME 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 the Cut/Fill Volumes between the Isopach Surface and the Zero Plane

27. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Obtaining Z-Values of the Isopach Triangle Vertically Non-Intersecting Planes

28. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt When Planes Collide Vertically Intersecting Planes

29. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt The Two Surfaces The Isopach Surface

30. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Apply the Simple Computation to All the 3D Triangles in the Model Above Below Intersecting Zero Plane (Recall Slide #21) The Isopach Surface

31. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt Surface-To-Surface Volume Report Surface1 Area = 10130.0 sq. m Surface2 Area = 10729.7 sq. m Overlapping Area = 10029.4 sq. m Unaffected Area = 0.0 sq. m Area of Cut = 4879.8 sq. m Area of Fill = 5149.6 sq. m Modified Area = 10029.4 sq. m Max Z = 33.5 m Min Z = 14.2 m Z Range = 19.3 m Cut Volume = 22198.39 Cubic Metres Fill Volume = 17509.36 Cubic Metres VOLUME REPORT USING THE COMPOSITE METHOD ON THE TWO SURFACES USED IN THIS PRESENTATION (Windows Application Written in C by H. Nandalal)

32. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt SURFACE TO SURFACE VOLUME REPORT Trimble 5475 Kellenburger Road Dayton, Ohio 45424-1099, USA 1-937-233-8921 Project: C:\Temp\tm.pro Report 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 as excavation. -------------------------------------------------------------------------------- Shrinkage/swell factors: Excavation 1.0000 Fill 1.0000 First Surface Number Second Surface Number 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 THE TWO SURFACES USED IN THIS PRESENTATION (Application: TerraModel)

33. Earthworks Volume Computation Algorithm CASLE Jamaica Regional and International Conference 10/10/12 H.A. Nandalal, Trinidad & Tobago Land Surveyor - www.survplan.com - nanco@tstt.net.tt I would like to thank: The Aubrey Barker Fund, Dr. Charisse Griffith-Charles & CASLE Atlantic Region for allowing me the opportunity to present this paper.