Virtual hand grasping is one of the core topics/techniques in virtual interaction

and it strongly determines the immersion. Given that real-time force analysis is complex

considerable rules that meet the characteristics of hand grasping are formulated instead of complex mechanic calculations. Some existing rules focus on the included angle of the normal vector of two contact points or the included angle of two lines that connect contact point and object center

but they cannot deal correctly with some shapes. This study proposes a shape-adaptive grasping method. This method uses the shape features and contact points of basic geometries

such as cube

sphere

and cylinder

to design grasping rules. 1) For a cube

at least three contact points that are not all collinear must be on the surface

and one of the included angles of the normal vector of every two contact points is larger than 90°. First

the positions of all contact points are determined. Second

the cube and all points are rotated; thus

every edge of the cube is parallel to the world axis

which simplifies the calculation. Third

whether the location of every point is on the plane

edge

or vertex of the cube is determined by the cube scale. Fourth

the normal vector of these points is calculated based on their locations. The vector direction is perpendicular to the plane when the point is on the plane or is the same as the moving direction of the point when the point is on the edge or vertex. Finally

the included angles of every two normal vectors are calculated

and the grasping result is determined. 2) For a sphere

at least four contact points exist

and the spatial relationship between these points and the sphere center should satisfy the proposition obtained from the analysis. First

the positions of the sphere center and all contact points are identified. Second

the center and every two of these points are used to form a plane

and whether all other points are on the same side of this plane is calculated. Finally

the grasping result is determined with the calculation results. 3) For a cylinder

depending on whether the contact points are all on the curved surface

a rule similar to sphere rule is used. First

the positions of all contact points are determined

and the cylinder and all the points are rotated so that the bottom plane of the cylinder parallels the world axis. Second

these points are projected to the bottom plane of the cylinder. Third

the circle center of the bottom plane and every projected point are used to form a diameter

and whether all other projected points are on the same side of the diameter is calculated. Finally

the grasping result is generated with the calculation results. When points exist on the top or bottom plane

the cube rule is used instead. This method can realistically handle the grasping of an object with a curved surface. For a complex object that can be composed by multiple basic geometries

our method divides the calculation into two steps. First

the object is decomposed into three basic geometries and then each geometry is calculated separately. Some geometries nearly meet the grasping rule

called unstable state. Second

our method selects each of these unstable state geometries

gathers information

such as the position and normal vector of all the points to it

and makes decisions on whether the entire object is caught with the basic geometry rules obtained before. Calculating the possibility of moment balance further reduces the occurrence of erroneous determinations. All normal vectors are the opposite direction of force

but their values are uncertain. The proposition obtained from the analysis implies that the moment may balance when the normal vectors meet a specific spatial relationship similar to the sphere rule. First

all normal vectors are normalized and projected to a unit sphere; thus

points exist on the surface. Second

the points are used to calculate the same proposition in sphere rule. Finally

whether the moment is balanced is determined. Only when both rules and moment balance are satisfied will the grasping be determined as a success. Experimental results show that the method can effectively handle the grasp of objects with curved surfaces

such as balls

and complex objects

such as cups

by using Unity3d software and Neuron Data Glove. When the virtual hand touches the upper hemisphere

the ball is not caught. Only if the figures ring around the ball will it be caught; casually grasping the cup will not catch it. Only when the gesture is correct and the moment is balanced can the cup be caught. This study proposes a shape-adaptive grasping method and a calculation method that decomposes complex objects into simple basic geometries. This method effectively handles the grasp and conforms to intuitive feel.