Method and apparatus for generating fillet surface between two surfaces

A method for generating a fillet surface which smoothly connects two surfaces to each other, using a three-dimensional (3D) computer-aided design (CAD) system, the method comprising the steps of:

• a) inputting information designating a spine curve which is located near a boundary between the two surfaces;
• b) using a shape modification part of the 3D CAD system, placing a circle on a normal plane of the spine curve at an arbitrary point on the spine curve, so that the circle is in contact with the two surfaces;
• c) using the shape modification part of the 3D CAD system, sliding the circle, while in contact with the two surfaces, to generate trajectories of two tangent points between the circle and the two surfaces, so that the fillet surface is defined by a trajectory of an outline of the circle and the trajectories of the two tangent points;
• and
• d) using the shape modification part of the 3D CAD system, generating a Gregory patch which approximately and parametrically represents the fillet surface, by using the trajectories of the two tangent points and the outline of the circle.

A method for generating a fillet surface which smoothly connects two surfaces to each other, using a three-dimensional (3D) computer-aided design (CAD) system, the method comprising the steps of:

• inputting information designating a spine curve defined by a parameter t near a boundary between the two surfaces;
• using a shape modification part of the 3D CAD system, equally dividing the spine curve into 2n parts;
• using the shape modification part of the 3D CAD system, placing 2n+1 number of circles each having a radius is expressed by a function having the parameter t, on 2n+1 number of normal planes of the spine curve at 2n+1 number of points on the spine curve, each of the points being defined by the parameter t=i/2n (i=0, 1, 2, . . . 2n+1, 2n), and each of the circles in contact with the two surfaces;
• using the shape modification part of the 3D CAD system, sliding each of the circles, while in contact with the two surfaces, in order to generate a movement vector representing how each of tangent points between each of the circles and the two surfaces moves when each of the circles slides;
• using the shape modification part of the 3D CAD system, generating n number of Bezier curves by each of the tangent points and the movement vector, the Bezier curves approximately and parametrically representing a trajectory of each of the tangent points;
• and
• using the shape modification part of the 3D CAD system, generating a Gregory patch which approximately and parametrically represents the fillet surface, by using the Bezier curve and an outline of each of the circles.

A three-dimensional (3D) computer aided design (CAD) apparatus which receives a geometric model representing a shape of a model, comprising:

• a) processing means for processing the geometric model;
• b) memory means, coupled to said processing means, for storing the the geometric model processed by said processing means;
• and
• c) reference means, coupled to said memory means, for extracting data stored in said memory means;
• wherein said processing means includes means for generating a fillet surface which smoothly connects two surfaces of the model to each other and includes:
• 1) drawing means for drawing spine curve near a boundary between the two surfaces;
• 2) setting means for placing a predetermined curve on a normal plane of the spine curve at an arbitrary point on the spine curve so that the predetermined curve is in contact with the two surfaces;
• 3) moving means for sliding the predetermined curve, while in contact with the two surfaces, in order to generate trajectories of two tangent points between the predetermined curve and the two surfaces, the fillet surface being defined by a trajectory of the predetermined curve and the trajectories of the two tangent points;
• and
• 4) fillet surface generating means for generating a parametric surface which approximately and parametrically represents the fillet surface, by using the trajectories of the two tangent points and the predetermined curve.

A three-dimensional (3D) computer aided design (CAD) apparatus which receives a geometric model representing a shape of a model, comprising:

• a) processing means for processing the geometric model;
• b) memory means, coupled to said processing means, for storing the geometric model processed by said processing means;
• and
• c) reference means, coupled to said memory means, for extracting data stored in said memory means:
• wherein said processing means includes means for generating a fillet surface which smoothly connects two surfaces of the model to each other and includes:
• 1) drawing means for drawing spine curve near
• a boundary between the two surfaces;
• 2) setting means for placing a circle on a normal plane of the spine curve at an arbitrary point on the spine curve so that the circle is in contact with the two surfaces;
• 3) moving means for sliding the circle, while in contact with the two surfaces, in order to generate trajectories of two tangent points between the circle and the two surfaces, the fillet surface being defined by a trajectory of the circle and the trajectories of the two tangent points;
• and
• 4) fillet surface generating means for generating a Gregory patch which approximately and parametrically represents the fillet surface, by using the trajectories of the two tangent points and the circle.

A three-dimensional (3D) computer aided design (CAD) apparatus which receives a geometric model representing a shape of a model, comprising:

• a) processing means for processing the geometric model;
• b) memory means, coupled to said processing means, for storing the geometric model processed by said processing means;
• and
• c) reference means, coupled to said memory means, for extracting data stored in said memory means;
• wherein said processing means includes means for generating a fillet surface which smoothly connects two surfaces of the model to each other and includes:
• 1) drawing means for drawing spine curve defined by a parameter t near a boundary between the two surfaces;
• 2) dividing means for equally dividing the spine curve into 2n parts;
• 3) setting means for placing 2n+1 number of circles each having a radius expressed by a function having the parameter t, on 2n+1 number of normal planes of the spine curve at 2n+1 number of points on the spine curve, each of the points being defined by the parameter t=i/2n (i=0, 1, 2, . . . 2n-1, 2n), and each of the circles is in contact with the two surfaces;
• 4) moving means for sliding each of the circles, while in contact with the two surfaces, in order to generate a movement vector representing how each of tangent points between each of the circles and the two surfaces moves when each of the circles slides;
• 5) approximately means for generating n number of Bezier curves by each of the tangent points and the movement vector, the Bezier curves approximately and parametrically representing a trajectory of each of the tangent points;
• and
• 6) fillet surface generating means for generating a Gregory patch which approximately and parametrically represents the fillet surface, by using the Bezier curve and an outline of each of the circles.