TIN surface

A TIN surface, short for triangulated irregular network, is a model of the ground made from points of known elevation joined into a mesh of triangles. Each triangle is flat, so the elevation anywhere on the site can be read from the triangle it falls in.

How it works

1. Collect points. Spot elevations, points along contour lines and survey shots each give an x, y position and an elevation.
2. Triangulate. The points are joined into triangles that do not overlap. Most software uses a method that avoids long, thin triangles where it can.
3. Add breaklines. Curbs, ridges, ditch bottoms and the tops and toes of slopes are drawn as lines the triangles cannot cross, so the surface follows sharp changes in grade.
4. Set a boundary. The surface stops at the edge of the area you care about, so triangles do not stretch across places with no data.

"Irregular" means the points do not have to sit on a grid. Dense points go where the ground changes and fewer where it is flat.

Example: reading an elevation

Say one triangle has corners at these points, in feet (example values):

The flat plane through them is: elevation = 100.0 + 0.2x + 0.1y.

At the point x = 4, y = 3, the elevation is 100.0 + 0.8 + 0.3 = 101.1 ft.

Example: volume between two surfaces

Earthwork software builds one TIN for existing grade and one for finished grade, then measures the space between them. Where both surfaces are flat over the same triangle, the volume is the triangle's area times the average of the depths at its three corners.

Say the triangle above has an area of 50 SF, and the cut depths at its corners are 1.0 ft, 2.0 ft and 1.5 ft (example values):

1. Average depth: (1.0 + 2.0 + 1.5) / 3 = 1.5 ft
2. Volume: 50 SF x 1.5 ft = 75 CF
3. Cubic yards: 75 CF / 27 = 2.8 CY of cut

Add up every triangle and you have the site's cut and fill.

What goes wrong

• A mistyped elevation makes a spike or a pit that adds false volume.
• Missing breaklines let triangles cut across a curb or a ditch and flatten it.
• Flat triangles form where three points sit on the same contour, often at the inside of a bend.
• No boundary lets the surface stretch past the survey and invent ground.

Looking at the surface before calculating catches most of these. In IntelCost's Earthwork tab, you build existing and finished grade surfaces from the contours and spot elevations on the plans, and you can show either one over the sheet to check it first. Volumes between two surfaces are in-place yards, cut in bank and fill compacted, so shrink and swell still apply. See cut and fill explained for the full method.