A
method
for
determining
a
zoom
path
between
predetermined
viewing
point
Pn+1
in
a
three-dimensional
(3D)
virtual
space
and
a
target
point
P0
in
the
3D
space,
the
target
point
having
an
integer
n≧2
of
predetermined
control
points
P1,
.
.
.
Pn
in
the
3D
space,
the
distance
between
Pk
to
P0
in
the
3D
space
being
less
than
the
distance
between
Pk+1
to
P0
in
the
3D
space
for
all
1
the
points
P0,
.
.
.
Pn
being
coplanar
the
method
comprising:

generating a nonlinear zoom path in the 3D space between the viewing point Pn+1 to the control point P1, the zoom path passing through the points P1, . . . , Pm, where m is an integer satisfying 1≦m≦n,

wherein

- a projection of the zoom path onto the plane containing points P0, . . . Pn has a continuous derivative, and

- at least one point on the zoom path has exactly two coordinates in common with a control point selected from the control points Pm+1, . . . , Pn.

generating a nonlinear zoom path in the 3D space between the viewing point Pn+1 to the control point P1, the zoom path passing through the points P1, . . . , Pm, where m is an integer satisfying 1≦m≦n,

wherein

- a projection of the zoom path onto the plane containing points P0, . . . Pn has a continuous derivative, and

- at least one point on the zoom path has exactly two coordinates in common with a control point selected from the control points Pm+1, . . . , Pn.

Text extracted from US-20110261052-A1

A
method
for
determining
a
zoom
path
between
predetermined
viewing
point
Pn+1
in
a
three-dimensional
(3D)
virtual
space
and
a
target
point
P0
in
the
3D
space,
the
target
point
having
an
integer
n≧2
of
predetermined
control
points
P1,
.
.
.
Pn
in
the
3D
space,
the
distance
between
Pk
to
P0
in
the
3D
space
being
less
than
the
distance
between
Pk+1
to
P0
in
the
3D
space
for
all
1
the
points
P0,
.
.
.
Pn
being
coplanar
the
method
comprising:

generating a nonlinear zoom path in the 3D space between the viewing point Pn+1 to the control point P1, the zoom path passing through the points P1, . . . , Pm, where m is an integer satisfying 1≦m≦n,

wherein

- a projection of the zoom path onto the plane containing points P0, . . . Pn has a continuous derivative, and

- a portion of the zoom path containing the points P1, . . . , Pm, is obtained by polynomial interpolation between Pk and Pk+1 for k=1 to m−1.

generating a nonlinear zoom path in the 3D space between the viewing point Pn+1 to the control point P1, the zoom path passing through the points P1, . . . , Pm, where m is an integer satisfying 1≦m≦n,

wherein

- a projection of the zoom path onto the plane containing points P0, . . . Pn has a continuous derivative, and

- a portion of the zoom path containing the points P1, . . . , Pm, is obtained by polynomial interpolation between Pk and Pk+1 for k=1 to m−1.

Text extracted from US-20110261052-A1