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2answers
45 views

How to prove this property of a projective transformation?

The copy below is from this book: Sophus Lie, Vorlesungen über Differentialgleichungen mit bekannten Infinitesimalen Transformationen, bearbeitet und herausgegeben von Dr. Georg Wilhelm ...
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2answers
113 views

Transformation matrix from quadrilateral to rectangle

There exists a rectangle somewhere in space with some orientation. A camera from the coordinate center point is looking along the z axis and is seeing the rectangle as a quadrilateral (due to ...
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1answer
67 views

Transforming a circle to get a parabola

On http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/geometry/geo-tran.html I am unable to understand the following point Obviously, this transformation sends (x,y,w)=(1,0,1) to (x',y',w') = ...
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1answer
33 views

Equation for a sphere after a projective transformation?

I was wondering if there is a general equation for a sphere that has undergone a projective transformation (i.e, the sphere has been multiplied by a 4x4 homography matrix)? I attempted to multiple ...
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1answer
131 views

How to project 3D plots on a 2D coordinate system without losing the metric scale?

I've been collection data of a river bank last week and I need to plot the cross sections of the data. The issue is, that the data taken consists of 3 coordinates: easting, northing and elevation. ...
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1answer
562 views

Finding a 3D transformation matrix based on the 2D coordinates

I have a square with the length of the sides being 1. This square is transformed by an unknown transformation matrix in the 3D space and then projected back to the plane (the projection is known). I ...
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2answers
44 views

Optimally projecting a point onto a line whose orientation is known

I have a line $l$ starting at origin ending at 0,0,1 along the $z$ axis. $l$ is rotated $P$ degrees around the $x$-axis and then $Q$ degrees around the $y$-axis. So I have a new endpoint for the line. ...