Abstract: A method for representing a moving object as it moves along a path in a three-dimensional coordinate system. A processor determines a direction of an animated motion of a three-dimensional object moving along a path from a starting location to a second location. The processor draws pairs of vectors from the starting location by performing a series of mathematical functions, where the tips of each pair of vectors identify two points of a three-dimensional mesh, and where the mathematical functions are functions of the starting location, of the location of a point on the object when the object is at the second location, and of the direction of motion of the object along the path. The processor further adjusts characteristics of the mesh and determines, as a function of the adjusted mesh, a characteristic of the animated object, such as its orientation in space, at the second location.

Abstract: A method for modeling and animating an object trajectory in three-dimensional (3D) space. The trajectory includes at least one course which represents a 3D model mesh. A course includes at least one segment which is a display unit of the 3D model mesh. A segment includes two 3D points. Multiple vertices are generated for a first 3D point of the segment to specify a plane such that a normal vector of the specified plane is parallel to a vector directed from the first 3D point of the segment to a second 3D point of the segment. The generated vertices are added to the 3D model mesh so that the generated vertices can be subsequently displayed as an extension of the 3D model mesh.

Abstract: A method for modeling and animating an object trajectory in three-dimensional (3D) space. The trajectory includes at least one course which represents a 3D model mesh. A course includes at least one segment which is a display unit of the 3D model mesh. A segment includes two 3D points. Multiple vertices are generated for a first 3D point of the segment to specify a plane such that a normal vector of the specified plane is parallel to a vector directed from the first 3D point of the segment to a second 3D point of the segment. The generated vertices are added to the 3D model mesh so that the generated vertices can be subsequently displayed as an extension of the 3D model mesh.