1. An object manipulation method of manipulating an object displayed on a display apparatus for deformation, the object manipulation method comprising: setting a manipulation area surrounding the object; capturing a moving image using a camera, the moving image comprising a manipulation instruction for the object within the manipulation area; determining an optical flow within the manipulation area based on frame images from the moving image; setting, by a control apparatus configured to control the display apparatus, a projecting polyhedron bounding the object, wherein the projecting polyhedron comprises a given point in the object being a center; dividing, by the control apparatus, the bounding polyhedron into a plurality of spaces inside the bounding polyhedron, with each of the plurality of spaces formed by vectors extending from the given point to apexes of the bounding polyhedron; for each vertex of the object: determining which space of the plurality of spaces each vertex is included in; projecting each vertex of the object onto each bounding vertex of the space each vertex is included to determine a decomposition coefficient for each bounding vertex; determining a motion vector in the manipulation area based on the optical flow; deforming the bounding polyhedron using the motion vector; calculating a new position of each vertex of the object based on the deformed bounding polyhedron and the decomposition coefficients; and displaying the object using the new position of each vertex of the object.