# Angle between normals of two planes

• Apr 6th 2013, 05:09 AM
roberto87
Angle between normals of two planes
Evening,

I have a bit of a conceptual problem modelling a real world interaction.

It involves the radiation received from a source. In this instance, let us say that the radiation source if a fire front (modelled at a snapshot in time as a wall of flame represented by a plane), and the receiver is the wall of a house (again modelled as a plane).
The wall of flame is moving in one direction at an angle to the ground determined by wind speed and direction and the house wall is not in the direct path of the fire front, off to the side in this instance at a different elevation.

I have the estimated radiation produced by the flame front but what I require is the angle between the normal of the flame front and the normal of the house wall.
I have been out of Uni for a while now and I'm a bit rusty but my idea was to:
1 - define an origin, bottom corner of wall or fire front
2 - take three points on the corners of the wall to construct two lines and use the cross product to determine the perpendicular
3 - do the same for the flame front (the width is limited by the vegetation and the height it determined by the fuel load)
4 - use the dot product on the two resulting perpendiculars as they were both calculated using the same origin

Am I on the right track here?
• Apr 6th 2013, 05:28 AM
majamin
Re: Angle between normals of two planes
Quote:

Originally Posted by roberto87
Evening,

I have a bit of a conceptual problem modelling a real world interaction.

It involves the radiation received from a source. In this instance, let us say that the radiation source if a fire front (modelled at a snapshot in time as a wall of flame represented by a plane), and the receiver is the wall of a house (again modelled as a plane).
The wall of flame is moving in one direction at an angle to the ground determined by wind speed and direction and the house wall is not in the direct path of the fire front, off to the side in this instance at a different elevation.

I have the estimated radiation produced by the flame front but what I require is the angle between the normal of the flame front and the normal of the house wall.
I have been out of Uni for a while now and I'm a bit rusty but my idea was to:
1 - define an origin, bottom corner of wall or fire front
2 - take three points on the corners of the wall to construct two lines and use the cross product to determine the perpendicular
3 - do the same for the flame front (the width is limited by the vegetation and the height it determined by the fuel load)
4 - use the dot product on the two resulting perpendiculars as they were both calculated using the same origin

Am I on the right track here?

That sounds correct. If a and b are your normals, then $\cos{\theta}=\frac{\bold{a}\cdot \bold{b}}{|\bold{a}||\bold{b}|}$.