Abstract: A computer-implemented method for constructing structures using beams bounded by quadric surfaces of revolution includes generating a quador beam within a computer-aided design (CAD) tool. The quador beam comprises two spheres at opposing endpoints, and the beam is bounded by a quadric surface of revolution around an axis of symmetry joining the center of the two spheres. The quadric surface of revolution abuts with tangent continuity with the surface of each of the spheres. Once generated, the quador beam can be visualized in the CAD tool or another display medium.

Abstract: A method, and corresponding systems and computer-readable mediums, for designing and manufacturing a part. A method includes receiving part data for a part to be manufactured. The method includes creating a set of balls and beams in a computer-aided design (CAD) model, in a patterning structure and based on the part data. The method includes constructing a steady lattice structure in the CAD model. The method includes displaying the CAD model including the steady lattice structure.

Abstract: Methods and systems are disclosed for a computer aided design system for designing multilevel lattice structures. A coarse lattice module defines a coarse lattice of balls connected by beams within a first boundary. A fine lattice module defines a fine lattice of balls connected by beams within a second boundary. The coarse lattice and the fine lattice have intersecting regions. A trimming module constructs a multilevel lattice structure according to a trimming operation based on the intersecting regions.

Abstract: A method, and corresponding systems and computer-readable mediums, for designing and manufacturing a part. A method includes receiving part data for a part to be manufactured. The method includes creating a set of balls and beams in a computer-aided design (CAD) model, in a patterning structure and based on the part data. The method includes constructing a steady lattice structure in the CAD model. The method includes displaying the CAD model including the steady lattice structure.

Abstract: A computer-implemented method for constructing structures using beams bounded by quadric surfaces of revolution includes generating a quador beam within a computer-aided design (CAD) tool. The quador beam comprises two spheres at opposing endpoints, and the beam is bounded by a quadric surface of revolution around an axis of symmetry joining the center of the two spheres. The quadric surface of revolution abuts with tangent continuity with the surface of each of the spheres. Once generated, the quador beam can be visualized in the CAD tool or another display medium.

Abstract: A method and system for segmenting tubular structures in 3D images is disclosed. User inputs identifying a first region on the image inside of a tubular structure and a second region of the image outside of the tubular structure are received. Based on this information, an ordered series of pearls are generated along the tubular structure. Pearls are spheres, each having a center location and a radius determined based on the center locations and radii of previous pearls and on local voxel intensities in the image. A continuous model of the tubular structure can be generated by interpolating the center locations and radii of the ordered series of pearls. The ordered series of pearls can be displayed and easily edited in response to user input, thus providing an efficient and flexible method for interactive segmentation of a potion of interest in a tubular structure.

Abstract: A method of computing a continuous interpolation of a discrete set of three-dimensional (3D) balls, including generating an initial skin, wherein the initial skin is a surface comprised of splines and wherein the splines touch each ball along a circle that is tangent to the ball, solving a first differential equation to minimize the initial skin's surface area or solving a second differential equation to minimize a squared mean curvature of the initial skin's surface, wherein the result of solving the first or second differential equations is an updated skin; and repeating the steps of solving the first or second differential equations for the updated skin, and then, repeating the steps of solving the first or second differential equations for each subsequently updated skin until a desired skin is realized.

Abstract: A method of computing a continuous interpolation of a discrete set of three-dimensional (3D) balls, including generating an initial skin, wherein the initial skin is a surface comprised of splines and wherein the splines touch each ball along a circle that is tangent to the ball, solving a first differential equation to minimize the initial skin's surface area or solving a second differential equation to minimize a squared mean curvature of the initial skin's surface, wherein the result of solving the first or second differential equations is an updated skin; and repeating the steps of solving the first or second differential equations for the updated skin, and then, repeating the steps of solving the first or second differential equations for each subsequently updated skin until a desired skin is realized.

Abstract: A method and system for segmenting tubular structures in 3D images is disclosed. User inputs identifying a first region on the image inside of a tubular structure and a second region of the image outside of the tubular structure are received. Based on this information, an ordered series of pearls are generated along the tubular structure. Pearls are spheres, each having a center location and a radius determined based on the center locations and radii of previous pearls and on local voxel intensities in the image. A continuous model of the tubular structure can be generated by interpolating the center locations and radii of the ordered series of pearls. The ordered series of pearls can be displayed and easily edited in response to user input, thus providing an efficient and flexible method for interactive segmentation of a potion of interest in a tubular structure.