- #1

wukunlin

Gold Member

- 414

- 99

## Main Question or Discussion Point

This may belong to the computing subforum, let me know if this is more true than having it here in the math forum :)

My questions are

1) Suppose there is a plane in 3D space and I have 3 points to define it:

and I want to put a particular point

What will be the most efficient way to compute the y- coordinate of

I can think of the nasty method which I compute the determinant of a 4x4 matrix to find the coefficients for:

Then substitute my known x and z, I get the feeling this is very inefficient and there are more elegant solutions than this. Are there any known algorithms to deal with this problem?

2) Now that I have my

for example, if

My questions are

1) Suppose there is a plane in 3D space and I have 3 points to define it:

**p**_{1}= {x_{1}, y_{1}, z_{1}}**p**_{2}= {x_{2}, y_{2}, z_{2}}**p**_{3}= {x_{3}, y_{3}, z_{3}}and I want to put a particular point

**p**_{4}which I already know the x- and z- coordinates.What will be the most efficient way to compute the y- coordinate of

**p**_{4}?I can think of the nasty method which I compute the determinant of a 4x4 matrix to find the coefficients for:

*ax + by + cz + z = 0*Then substitute my known x and z, I get the feeling this is very inefficient and there are more elegant solutions than this. Are there any known algorithms to deal with this problem?

2) Now that I have my

**p**_{4}, I want have the same relative position to the 3 points**p**_{1},**p**_{2},**p**_{3}if someone move this triangle around:*f(***p**_{1},**p**_{2},**p**_{3}) =**p**_{4}for example, if

**p**_{4}happens to be in the middle of the triangle, the function would be the average of each of the*x, y, z*coordinates of the 3 points. But for a point that is off-centered, how will I go about finding what this function should be?