Calculating Perpendicular Point on a Line in 2D Plane

[Asuralm]

Hi all:

Given a line L:v= v0+t*n; and two points A, B in 2D plane; A and B are on the two sides of the line L. I want to calculate the point C which makes AC is perpendicular to BC

I know it's simply that substitude v to C and <AC, BC>=0. But I don't know how to simplify the equation.

Could anyone help me please?

Thanks

 

[HallsofIvy]

Hi all:

Given a line L:v= v0+t*n; and two points A, B in 2D plane; A and B are on the two sides of the line L. I want to calculate the point C which makes AC is perpendicular to BC

C is on L?

I know it's simply that substitude v to C and <AC, BC>=0. But I don't know how to simplify the equation.

Could anyone help me please?

Thanks

The vector AC= v0+ t*n is given by v0+ t*n-A. The vector BC is given by v0+ t*n- B.
Their inner product <AC,BC>= <v0+ t*n- A,v0+ t*n- B>= |v0- t*n|²- <v0+ t*n,A+B>+ <A,B>.
Without specific values for A and B, v0 and n, I don't see how you can get any simpler than that.

 

[Asuralm]

should this |v0- t*n|2- <v0+ t*n,A+B>+ <A,B>

be <v0+t*n, v0+t*n> - <v0+t*n, A+B> + <A, B> ?