Tofhesseplane

by Tim C. Lueth, SG-Lib Toolbox: SolidGeometry 5.6 - Analytical Geometry
Introduced first in SolidGeometry 5.2, Creation date: 2022-06-19, Last change: 2025-09-15

returns an HT amtrix from a hesse normal form of a plane

See Also: TofPez , hesseplaneofT

Example Illustration

Syntax

T=Tofhesseplane([d,ez,T0])

Input Parameter

`d`:		distance to plane
`ez`:		ez vector of plane
`T0`:		optional relative plane that is used for d and ez; default is eye(4)

Output Parameter

T: HT matrix of plane

Examples


Tofhesseplane(5,[0.8 0.4 0.4])					% relative to T=eye(4)
Tofhesseplane(5,[1 1 1],   TofPez([0 0 -10],[0 0 1]))       % with respect to a plane at [0 0 -10]

Copyright 2022-2025 Tim C. Lueth. All rights reserved. The code is the property of Tim C. Lueth and may not be redistributed or modified without explicit written permission. This software may be used free of charge for academic research and teaching purposes only. Commercial use, redistribution, modification, or reverse engineering is strictly prohibited. Access to source code is restricted and granted only under specific agreements. For licensing inquiries or commercial use, please contact: Tim C. Lueth

Algorithm (Workflow)

This function, Tofhesseplane, computes a homogeneous transformation (HT) matrix from the Hesse normal form of a plane. It is part of the SolidGeometry library and was introduced in version 5.2.

Input Parameters

d: The distance to the plane. It is a scalar value representing how far the plane is from the origin along the normal vector.
ez: The normal vector of the plane. It is a 3-element vector that is normalized within the function to ensure it has a unit length.
T0: An optional parameter representing a relative plane. It is a 4x4 matrix used as a reference for the distance and normal vector. If not provided, it defaults to the identity matrix eye(4).

Output

T: The resulting HT matrix of the plane. It is a 4x4 matrix that represents the transformation of the plane in 3D space.

Algorithm Steps

Retrieve the input parameters using the getfuncparams function. This function extracts the parameters from the input arguments, providing default values if necessary.
Normalize the ez vector to ensure it is a unit vector. This is done by dividing the vector by its norm.
Compute the HT matrix T using the TofPez function. This function takes the product of d and ez as the position vector and ez as the normal vector.
Multiply the resulting matrix T by T0 to account for any relative transformation specified by T0.
If no output is requested (i.e., nargout==0), call the hesseplaneofT function to display or process the resulting transformation matrix T with respect to T0.

Example Usage

Here are two examples of how to use the Tofhesseplane function:

Tofhesseplane(5, [0.8, 0.4, 0.4]): Computes the HT matrix for a plane 5 units away from the origin with a normal vector of [0.8, 0.4, 0.4], relative to the identity matrix.
Tofhesseplane(5, [1, 1, 1], TofPez([0, 0, -10], [0, 0, 1])): Computes the HT matrix for a plane 5 units away with a normal vector of [1, 1, 1], relative to another plane located at [0, 0, -10] with a normal vector of [0, 0, 1].

Algorithm explaination created using ChatGPT on 2025-08-18 23:37. (Please note: No guarantee for the correctness of this explanation)

Last html export of this page out of FM database by TL: 2025-09-21