Asuralm
May15-09, 10:43 AM
Hi all:
Assume in 3D space there is a point [latex]v=[v_x, v_y, v_z][/tex], and a normal vector associate with it as n=[n_x, n_y, n_z]. A line function is defined as u=w+t\cdot l where w=[w_x, w_y, w_z] is a point, and l=[l_x, l_y, l_z] is the normalized direction of the line. l and n are normalized. Assume there is a function defined as:
K = \frac{(u-v)\cdot n}{||u-v||^2}
My question is when point u varies on the line, is the function K varies monotonically???
I've tried to compute \frac{dK}{dt}, but I can't really see if it's monotone or not, can some one help me please?
Thanks
Assume in 3D space there is a point [latex]v=[v_x, v_y, v_z][/tex], and a normal vector associate with it as n=[n_x, n_y, n_z]. A line function is defined as u=w+t\cdot l where w=[w_x, w_y, w_z] is a point, and l=[l_x, l_y, l_z] is the normalized direction of the line. l and n are normalized. Assume there is a function defined as:
K = \frac{(u-v)\cdot n}{||u-v||^2}
My question is when point u varies on the line, is the function K varies monotonically???
I've tried to compute \frac{dK}{dt}, but I can't really see if it's monotone or not, can some one help me please?
Thanks