Techniques for determining a swept volume of an object moving along a trajectory in a 3D space are disclosed. In some examples, a computer graphics application accesses a representation of the object, such as the signed distance field (SDF), and the trajectory information describing the movement path in the 3D space over a time period. The 3D space is represented using a grid of voxels each having multiple vertices. The computer graphics application determines the swept volume of the object in the 3D space by evaluating a subset of the grid of voxels (e.g., the voxels surrounding the surface of the swept volume). The number of voxels in the subset of voxels is less than the number of voxels in the grid of voxels. The computer graphics application further generates a representation of the swept volume surface for output.

A differentiable simulator for simulating the cutting of soft materials by a cutting instrument is provided. In accordance with one aspect of the disclosure, a method for simulating a cutting operation includes: receiving a mesh for an object, modifying the mesh to add virtual nodes associated with a predefined cutting plane, optimizing a set of parameters associated with a simulator based on ground-truth data, and running a simulation via the simulator to generate outputs that include trajectories associated with a cutting instrument. Optimizing the set of parameters can include performing inference based on a set of ground-truth trajectories captured using sensors to measure real-world cutting operations. The inference techniques can employ stochastic gradient descent, stochastic gradient Langevin dynamics, or a Bayesian approach. In an embodiment, the simulator can be utilized to generate control signals for a robot based on the simulated trajectories.

A medical system includes: an endoscope and at least one treatment tool; a treatment-tool coordinate calculating unit that extracts the treatment tool by processing two or more images acquired at different times by the endoscope, that determines directions of longitudinal axes of the extracted treatment tool, and that calculates a coordinate of an intersection of the determined two or more longitudinal axes; and a judgment unit that judges whether the treatment tool serves as a follow target, on the basis of the coordinate of the intersection calculated by the treatment-tool coordinate calculating unit.

A method and an intersection testing module in a ray tracing system for determining whether a ray intersects a three-dimensional axis-aligned box. It is determined whether a first condition is satisfied, wherein the first condition is, or is equivalent to,

[00001]$.Math.C_x-C_z\frac{D_x}{D_z}.Math.\le H_z\frac{D_x}{D_z}+H_x.$

It is determined whether a second condition is satisfied, wherein the second condition is, or is equivalent to,

[00002]$.Math.C_y-C_z\frac{D_y}{D_z}.Math.\le H_z\frac{D_y}{D_z}+H_y.$

It is determined whether a third condition is satisfied, wherein the third condition is, or is equivalent to,

[00003]

There is described herein systems and methods for camera colliders and shot composition preservation within a 3D virtual environment that prevent a virtual procedural camera from getting stuck behind an object, or penetrating into an object, when filming a subject, while at the same time also maintaining the screen composition of the subject in the camera shot.

A computing device comprises a memory and a control unit coupled to the memory. The control unit is configured to receive a patient model and identify a plurality of port locations on the patient model for accessing a workspace using a plurality of instruments controlled by a computer-assisted device. For each of the port locations, the control unit determines a collision volume for portions of the computer-assisted device proximal to the port location, a reachability metric, and an anthropomorphic metric. For each combination of the plurality of port locations, the control unit determines a collision metric based on overlaps of the collision volumes for the port locations in the combination, and an aggregate metric for the combination. The control unit is also configured to display one or more of the combinations of the plurality of port locations to a user along with a corresponding aggregate metric.

Disclosed is a method for predicting collisions and conflicts between multiple moving bodies. A method for predicting and avoiding collisions and conflicts between multiple moving bodies comprises the steps of: creating objects by modeling the shape of each of multiple moving bodies; creating two-dimensional circles by modeling the objects by using size information of the objects; modeling the two-dimensional circles into moving disks by using at least one of the moving speeds of the moving bodies, the monitoring time window for the moving bodies, and the size information of the two-dimensional circles; computing a Voronoi diagram between the moving disks and calculating edges of the Voronoi diagram; and during the monitoring time window for the moving bodies, calculating a flipping event in which at least one of the edges of the Voronoi diagram is converted into a vertex and then converted into another edge, and a collision event by which a collision between a pair of moving disks defining an edge of the Voronoi diagram is predicted, and calculating whether actual collisions occur between moving disks triggering the flipping event and between moving disks triggering the collision event, in chronological order of the occurrence of the flipping event and the collision event.

A method and an intersection testing module in a ray tracing system for performing intersection testing for a ray with respect to a plurality of convex polygons, each of which is defined by an ordered set of vertices, wherein at least one of the vertices is a shared vertex which is used to define at least two of the convex polygons. The vertices of the convex polygons are projected onto a pair of axes orthogonal to the ray direction. A vertex ordering scheme defines an ordering of the projected vertices which is independent of the ordering of the vertices in the ordered sets. For each of the convex polygons, for each edge of the convex polygon defined by two of the projected vertices, a parameter indicative of which side of the edge the ray passes on is determined, wherein if the ray is determined to intersect a point on the edge then the parameter is determined based upon whether the ordering of the projected vertices defining the edge matches the ordering of the vertices in the ordered set of vertices defining the convex polygon. Whether the ray intersects the convex polygon is determined based on the parameters determined for the edges of the convex polygon.

Techniques are disclosed for improving the throughput of ray intersection or visibility queries performed by a ray tracing hardware accelerator. Throughput is improved, for example, by releasing allocated resources before ray visibility query results are reported by the hardware accelerator. The allocated resources are released when the ray visibility query results can be stored in a compressed format outside of the allocated resources. When reporting the ray visibility query results, the results are reconstructed based on the results stored in the compressed format. The compressed format storage can be used for ray visibility queries that return no intersections or terminate on any hit ray visibility query. One or more individual components of allocated resources can also be independently deallocated based on the type of data to be returned and/or results of the ray visibility query.

Techniques for placing and manipulating multiple three-dimensional (3D) models using mobile augmented reality (AR) are described. One technique includes receiving a first request to initialize an AR simulation of a first product for sale within a physical environment. In response to the first request, a first 3D model of the first product for sale is rendered onto the screen. After rendering the first 3D model, a second request to visualize a second product for sale within the physical environment is received during the AR simulation of the first product for sale. In response to the second request, a second 3D model of the second product for sale is rendered onto the screen with the first 3D model.