- #1
Asuralm
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Hi all:
Assume in 3D space there is a point 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:<br /> <br /> <br /> K = \frac{(u-v)\cdot n}{||u-v||^2}<br /><br /> <br /> My question is when point u varies on the line, is the function K varies monotonically?<br /> <br /> 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?<br /> <br /> Thanks
Assume in 3D space there is a point 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:<br /> <br /> <br /> K = \frac{(u-v)\cdot n}{||u-v||^2}<br /><br /> <br /> My question is when point u varies on the line, is the function K varies monotonically?<br /> <br /> 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?<br /> <br /> Thanks
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