Embedded Files
Meeting on 10/12
Meeting on 10/12
Goal
Goal
1. with given vertices in 3D
- Fitting a plane to a set of points in 3D/ Detecting set of planes from point clouds
- project vertices into plane (shaking hands)
- distance of a point to plane
- check whether a point is in the shape
Quaternion(x, y, z, w)
Quaternion(x, y, z, w)
Reference: BodyFrame.FloorClipPlane Property
- (x,y,z) components are a unit vector indicating the normal of the plane
- w is the distance from the plane to the origin in meters.
Ransac algorithm for detecting planes in a set of points
Ransac algorithm for detecting planes in a set of points
"Random sample consensus, or RANSAC, is an iterative method for estimating a mathematical model from a data set that contains outliers. The RANSAC algorithm works by identifying the outliers in a data set and estimating the desired model using data that does not contain outliers."
Ref: Detecting set of planes from point cloud
- Pick 3 points at random.
- Make a plane.
- Check if each other point lies on the plane.
- If enough are on the plane - recalculate a best plane from all these points and remove them from the set
- If not try another 3 points
- Stop when you have enough planes, or too few points left.
Given a set of points (3D) this function computes the plane that fits best those points by minimizing the sum of the quadratic distances (perpendicular to the plane) between the plane and the points.
The fit is performed by computing the eigen-values/vectors associated to the distribution of points.
Three points (A,B,C) can define two distinct vectors AB and AC. Since the two vectors lie on the plane, their cross product can be used as a normal to the plane.
- Determine the vectors
- Find the cross product of the two vectors
- Substitute one point into the Cartesian equation to solve for d.
Cross product
Cross product
Three points will lie on same line if sum of the distance between first and second points, and distance between second and third points, is equal to the distance between first and third point
Find the projection of a point onto a plane
Find the projection of a point onto a plane
The projection of a point projPt = (x, y, z) onto a plane given by a point planePt = (d, e, f) and a normal n = (a, b, c) is
projection = projPt - dot(projPt - planePt, n) * n(This calculation assumes that n is a unit vector.)
3d math functions provided by Unity
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