Both lines have the length 9. You call this new kind of line taxicab-line or t-line. There is the question, how many t-line segments are between two points. You can count them in this simple case.
There are 6 of them. Looking at the number of t-lines systematically, you discover a law. The number of t-line segments on a crossing is always the sum of the segments at the foregoing crossings. This leads to Pascal's triangle, whose rows are diagonal here. There are 84 t-lines for the case "6 to the right, 3 to the top" to go from A to B.
For the sake of completeness here is any line between A and B, which is not a t-line segment. Here are two t-line segments of the length 8 between the points A and B. You get a 2-gon, which doesn't exist in the Euclidean geometry. You can go a step forward and call the t-quadrilateral ADBC a t-rhombus, because four sides are equal. There is a problem in this definition. Many features of the rhombus get lost, for example the symmetry.
In this sense the quadrilaterals on the left are t-squares. If you connect the points by straight lines, you get a rhombus.
Geometrie für Dummies (German Edition) by Wendy Arnone,Markus Steffen - Dino Salvatore E-books
Thus is it a t-rhombus and no t-square? If you demand all features of the square, you must only take the square of the Euclidean geometry as t-square. You get a t-line from a t-line segment, if you elongate the t-line segment over both ends. You must mind that it goes always upwards here or downwards. If you look for points of intersections between two t-lines, you can have each number of points.
Here the two t-lines intersect in two points.
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Initially, the cars were checked with a mechanically-based coordinate measuring machine. Optical systems, in contrast, provide userindependent and reproducible results, responding to the increasing requirements of automobile manufacturers. To remain competitive on the market with regard to 3D measuring systems, Continental chose the ProCam to implement its structural deformation analyses.
The system provides fast and accurate results even in poorly accessible points.
Only one orientation RPS transformation is necessary for measurement of the entire vehicle. The hand-held ProCam probe is configurable with interchangeable measuring tips with which the points to be measured are probed. The preparation box in Alzenau is equipped as a ProCam measurement space. Test preparation and 3D measurement can thus take place in one room, where the entire vehicle is fitted with testing equipment and geometrically measured with ProCam: Body, structural and safety-relevant components, interior, dashboard, single points, determination of contours.
The vehicle coordinate system for subsequent dummy positioning in the relevant door cut-out areas are marked with targets and their 3D positions are determined by the ProCam system. This saves time on the well-utilized crash track.
Five-dimensional space
After the car crash, measurements are repeated with the ProCam system. The evaluation software AICON 3D Studio automatically creates a structural deformation analysis, which determines the individual deformations at the preliminary measurement points. In the measurement report, the deformations are clearly visualized in overview images with vectors, which can be broken down into individual components X, Y, Z.
MoveInspect DPS used for sled and crash tests The measurement system for online 3D dummy positioning is used at Continental for multiple applications, for example in full-size crashes with complete vehicles and in sled testing with car bodies or body-inwhite for component and airbag testing. The mobile system is simple to use at a variety of locations. Its advantages include speed, since all the points marked on the dummy head, H-point, knees are simultaneously captured and deviations from the target position are displayed in real-time.