MATLAB: How to calculate the point of intersection of two lines in 3D space

Mapping ToolboxMATLAB

How can I calculate the intersection of two 3-dimensional lines?

Best Answer

First of all, in 3D space, note that two non-identical lines would not have an intersection point unless they are coplanar. If they are not coplanar, then a "best intersection point" can be estimated, e.g. in a least-squares sense.

https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection

For example, either of the following File Exchange functions can be used to perform this calculation:

a) https://www.mathworks.com/matlabcentral/fileexchange/37192-intersection-point-of-lines-in-3d-space

b) https://www.mathworks.com/matlabcentral/fileexchange/59805-line-line-intersection-n-lines-d-space

Please note that these were not authored by MathWorks. In case you have questions specifically about the above 3rd-party File Exchange packages, we would recommend to contact the respective authors.

As an aside, for the 2D case, two non-identical lines will have an intersection unless they are parallel. On approach to calculate the intersection of two 2D lines is to utilize the "polyxpoly" function from the Mapping Toolbox:

https://www.mathworks.com/help/map/ref/polyxpoly.html

Here is another helpful reference page from the Mapping Toolbox documentation:

https://www.mathworks.com/help/map/vector-intersections.html

Related Solutions

MATLAB: How to plot a map and calculate distance between two points in the Geographic Space

Showing the map in a figure There are different projections as shown in documentation page in https://www.mathworks.com/help/map/summary-and-guide-to-projections.html. You can choose the most appropriate for your workflow.

You can plot latitude and longitude points, e.g. 52.229588, 0.150855, using "geoshow" function as shown in documentation page in https://www.mathworks.com/help/map/ref/geoshow.html. Here is an example:

>> figure
>> geoax = axesm('pcarree');
>> geoshow('landareas.shp', 'FaceColor', [0.5 1.0 0.5]);
>> geoshow(52.229588, 0.150855, 'DisplayType', 'Point', 'Marker', '+', 'Color', 'red');
>> geoshow(42.301853, -71.376126, 'DisplayType', 'Point', 'Marker', '+', 'Color', 'red');

The figure will have a map which is draggable, and will have a red cross in Cambridge, UK. The figure allows to zoom in closer, to zoom out and to drag around the map.

Distance between two points in the Geographic Space You can calculate the distance between two points, as shown in documentation page in https://www.mathworks.com/help/map/calculate-distance-between-two-points-in-geographic-space.html, https://www.mathworks.com/help/map/ref/distance.html.

For the example, let us choose two GPS points:

52.229588, 0.150855 in Cambridge, UK.
42.301853, -71.376126 in Natick, MA, USA.

Then the arc length distance can be computed in this way:

[arclen, az] = distance([52.229588, 0.150855], [42.301853, -71.376126])
arclen =
   47.5027
az =
  287.9302

Then the distance can be calculated in kilometres using "deg2km" function as shown in documentation page in https://www.mathworks.com/help/map/ref/deg2km.html.

>> km = deg2km(arclen)
km =
   5.2821e+03

MATLAB: How to find the intersection point of two lines in MATLAB 6.5 (R13)

Currently, there is no function in MATLAB that allows you to find intersection of any two lines or line segments. If you know that two lines in 2D intersect (are not skew) and you know two points on each of those lines, you can find the intersection using the following formula:

% Sample data
L1_x1 = 1;
L1_y1 = 2;
L1_x2 = 3;
L1_y2 = 4;
L2_x1 = 1;
L2_y1 = 4;
L2_x2 = 3;
L2_y2 = 3;
% Plot the lines
plot([L1_x1 L1_x2], [L1_y1 L1_y2])
hold on
plot([L2_x1 L2_x2], [L2_y1 L2_y2])
% Compute several intermediate quantities
Dx12 = L1_x1-L1_x2;
Dx34 = L2_x1-L2_x2;
Dy12 = L1_y1-L1_y2;
Dy34 = L2_y1-L2_y2;
Dx24 = L1_x2-L2_x2;
Dy24 = L1_y2-L2_y2;
% Solve for t and s parameters
ts = [Dx12 -Dx34; Dy12 -Dy34] \ [-Dx24; -Dy24];
% Take weighted combinations of points on the line
P = ts(1)*[L1_x1; L1_y1] + (1-ts(1))*[L1_x2; L1_y2];
Q = ts(2)*[L2_x1; L2_y1] + (1-ts(2))*[L2_x2; L2_y2];
% Plot intersection points
plot(P(1), P(2), 'ro')
plot(Q(1), Q(2), 'bo')
hold off

P and Q both contain the values of the common intersection point.

Alternately, if you have discrete data and know that some point is in data sets for both lines, you can use the "intersect" function.

Finally, if you own the "Mapping Toolbox" for MATLAB, you can use the "polyxpoly" function to calculate the intersection point.

For more information on these or any other command, type the following at the MATLAB command prompt:

help function_name
% or
doc function_name
%where function_name is the name of the function of interest

Best Answer

Related Solutions

MATLAB: How to plot a map and calculate distance between two points in the Geographic Space

MATLAB: How to find the intersection point of two lines in MATLAB 6.5 (R13)

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