Triangulation in research means using multiple datasets, methods, theories, and/or investigators to address a research question. It's a research strategy that can help you enhance the validity and credibility of your findings and mitigate the presence of any research biases in your work..
What is the geometric technique of triangulation?
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points..
What is the principle of triangulation in geometry?
The principal of triangulation is as follows: i) If we know one side and two angles (three angles) of a triangle then the remaining sides can be determined. ii) If we know direction of one side then the direction of remaining sides can be make up accurately..
What is triangulation in computational geometry?
Polygon triangulation is an essential problem in computational geometry because working with a set of triangles is faster than working with an entire polygon in case of complex graphics. Polygons are very convenient for computer representation of real world object boundaries..
What is triangulation in geo informatics?
[surveying] Locating positions on the earth's surface using the principle that if the measures of one side and the two adjacent angles of a triangle are known, the other dimensions of the triangle can be determined..
What is triangulation in geometry?
In trigonometry and geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly..
What is triangulation in geometry?
Triangulation is the division of a surface or plane polygon into a set of triangles, usually with the restriction that each triangle side is entirely shared by two adjacent triangles..
Where did triangulation come from?
The idea of triangulation was apparently conceived by the Danish astronomer Tycho Brahe before the end of the 16th century, but it was developed as a science by a contemporary Dutch mathematician, Willebrord van Roijen Snell..
Where is triangulation used in the real world?
Triangulation today is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision, model rocketry and, in the military, the gun direction, the trajectory and distribution of fire power of weapons. The use of triangles to estimate distances dates to antiquity..
In computer vision, triangulation refers to the process of determining a point in .
D space given its projections onto two, or more, images
The principal of triangulation is as follows: i) If we know one side and two angles (three angles) of a triangle then the remaining sides can be determined. ii) If we know direction of one side then the direction of remaining sides can be make up accurately.
[surveying] Locating positions on the earth's surface using the principle that if the measures of one side and the two adjacent angles of a triangle are known, the other dimensions of the triangle can be determined.
In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P. Triangulations may be viewed as special cases of planar straight-line graphs.
Polygon triangulation is an essential problem in computational geometry because working with a set of triangles is faster than working with an entire polygon in case of complex graphics. Polygons are very convenient for computer representation of real world object boundaries.
In computational geometry, a constrained Delaunay triangulation is a generalization of the Delaunay triangulation that forces certain required segments into the triangulation as edges, unlike the Delaunay triangulation itself which is based purely on the position of a given set of vertices without regard to how they should be connected by edges. It can be computed efficiently and has applications in geographic information systems and in mesh generation.
Computational geometry triangulation
Triangulation method
In mathematics and computational geometry, a Delaunay triangulation (DT), also known as a Delone triangulation, for a given set texhtml >{pi} of discrete points texhtml >pi in general position is a triangulation such that no point texhtml >pi is inside the circumcircle of any triangle in the DT. Delaunay triangulations maximize the minimum of all the angles of the triangles in the triangulation; they tend to avoid sliver triangles. The triangulation is named after Boris Delaunay for his work on this topic from 1934.
Point set triangulation minimizing total length
In computational geometry and computer science, the minimum-weight triangulation problem is the problem of finding a triangulation of minimal total edge length. That is, an input polygon or the convex hull of an input point set must be subdivided into triangles that meet edge-to-edge and vertex-to-vertex, in such a way as to minimize the sum of the perimeters of the triangles. The problem is NP-hard for point set inputs, but may be approximated to any desired degree of accuracy. For polygon inputs, it may be solved exactly in polynomial time. The minimum weight triangulation has also sometimes been called the optimal triangulation.
A triangulation of a set of points mwe-
A triangulation of a set of pointsmwe-math-element> in the Euclidean space mwe-math-element> is a simplicial complex that covers the convex hull of mwe-math-element>, and whose vertices belong to mwe-math-element>. In the plane, triangulations are made up of triangles, together with their edges and vertices. Some authors require that all the points of mwe-math-element> are vertices of its triangulations. In this case, a triangulation of a set of points mwe-math-element> in the plane can alternatively be defined as a maximal set of non-crossing edges between points of mwe-math-element>. In the plane, triangulations are special cases of planar straight-line graphs.
In computational geometry
Partition of a simple polygon into triangles
In computational geometry, polygon triangulation is the partition of a polygonal area texhtml mvar style=font-style:italic>P into a set of triangles, i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is texhtml mvar style=font-style:italic>P.
Triangulation (disambiguation)
Topics referred to by the same term
Triangulation is the process of determining the location of a point by forming triangles to it from known points.
Subdivision of a planar object into triangles
In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices. Triangulations of a three-dimensional volume would involve subdividing it into tetrahedra packed together.
