Cuboid and cylinder space collision detection method

Abstract

The invention discloses a cuboid and cylinder space collision detection method, which comprises the following steps: based on a preset projection axis set, respectively calculating projection intervals of a cylinder and a cuboid on each projection axis in the preset projection axis set by adopting a projection axis method; if at least one projection axis which enables the projection interval of the cylinder to be not overlapped with the projection interval of the cuboid exists in the preset projection axis set, judging that the cylinder and the cuboid do not collide with each other; and if the projection axis which enables the projection interval of the cylinder to be not overlapped with the projection interval of the cuboid does not exist in the preset projection axis set, judging whether the cylinder collides with the cuboid or not by adopting projection surface convex hull detection. The efficiency and the accuracy of collision detection are effectively considered by comprehensively applying a staged strategy combining rapid projection axis elimination and precise projection surface convex hull judgment.

Description

A method for detecting spatial collisions between cuboids and cylinders Technical Field

[0001] This invention relates to the field of robotic arm control technology, and in particular to a method for detecting spatial collisions between cuboids and cylinders. Background Technology

[0002] In the field of robot motion planning and control, collision detection is a crucial fundamental technology. Its purpose is to pre-determine whether there is a risk of interference between the robot itself or the geometric envelope of its working environment, thereby avoiding physical collisions and ensuring the safety of equipment and personnel. Cylinders and cuboids, as two of the most basic and commonly used geometric shapes, are often used to simplify the representation of robotic arm links, end effectors, and obstacles in the work environment. Therefore, researching efficient and accurate collision detection algorithms between cuboids and cylinders has direct engineering value for improving the reliability and real-time performance of robot systems.

[0003] Currently, several mainstream methods are widely used for collision detection of regular geometric shapes. The projection axis method (or the separating axis theorem) is often preferred due to its high computational efficiency. The core of this method is to find a projection axis such that the projection regions of the two objects on this axis do not overlap, thus quickly determining that they are separated. However, the effectiveness of this method is highly dependent on the completeness of the available projection axes. For specific combinations such as cylinders and cuboids, it may be impossible to find all potential projection axes, leading to missed detections—that is, a collision may have theoretically occurred, but the algorithm failed to recognize it.

[0004] Another common method is the projection plane method. This method determines collisions by projecting a 3D object onto a specific plane and analyzing the projection relationship in 2D space. While this method theoretically provides more comprehensive detection, its computational process is usually more complex. It requires finding a suitable projection plane, calculating the projected convex hull, and analyzing the relationship between the convex hull and the origin. The entire process has a high computational cost, making it difficult to meet the needs of applications with high real-time requirements.

[0005] Furthermore, algebraic methods offer the highest accuracy by using precise mathematical calculations to determine the closest distances or even the coordinates of the closest points between geometric objects. However, this precise calculation comes at the cost of an extremely heavy computational burden and a long processing time, making it unsuitable for robot control systems that require high-frequency, real-time collision detection. Summary of the Invention

[0006] The purpose of this invention is to provide a method for detecting collisions between cuboids and cylinders in space. By comprehensively utilizing a phased strategy that combines rapid elimination of collisions along the projection axis with precise determination of the convex hull of the projection surface, the method effectively balances the efficiency and accuracy of collision detection.

[0007] To address the aforementioned technical problems, a first aspect of this invention provides a spatial collision detection method for a cuboid and a cylinder, comprising the following steps: based on a preset set of projection axes, calculating the projection intervals of the cylinder and the cuboid on each projection axis in the preset set of projection axes using the projection axis method; if there exists at least one projection axis in the preset set of projection axes that prevents the projection intervals of the cylinder and the cuboid from overlapping, then determining that the cylinder and the cuboid have not collided; if there is no projection axis in the preset set of projection axes that prevents the projection intervals of the cylinder and the cuboid from overlapping, then determining whether the cylinder and the cuboid have collided using projection surface convex hull detection.

[0008] Further, the preset projection axis set includes: a first projection axis subset, a second projection axis subset, a third projection axis subset, and a fourth projection axis subset; the first projection axis subset includes the axial vector of the cylinder per unit length; the second projection axis subset includes three mutually orthogonal unit direction vectors of the cuboid; the third projection axis subset includes three vectors obtained by performing a cross product operation between the axial vector of the cylinder and each of the unit direction vectors of the cuboid; the fourth projection axis subset includes several direction vectors determined by drawing perpendicular lines from multiple vertices of the cuboid to the axis of the cylinder.

[0009] Further, the step of using projection plane convex hull detection to determine whether the cylinder and the cuboid collide includes: transforming the cuboid into a cylindrical coordinate system established with the cylinder as the center, and obtaining the coordinates of the transformed cuboid vertices; based on the transformed cuboid vertices coordinates and the height information of the cylinder, obtaining a set of feature points of the cuboid within the height range of the cylinder; projecting the set of feature points onto a plane perpendicular to the axis of the cylinder to form a two-dimensional projection point set, and constructing a two-dimensional convex hull based on the two-dimensional projection point set; and determining whether the cylinder and the cuboid collide based on the position and distance relationship between the projection points of the cylinder's central axis and the two-dimensional convex hull.

[0010] Further, determining whether the cylinder and the cuboid collide based on the position and distance relationship between the projection point of the cylinder's central axis and the two-dimensional convex hull includes: determining whether the projection point of the cylinder's central axis is located inside the two-dimensional convex hull; if the projection point is located inside the two-dimensional convex hull, then determining that the cylinder and the cuboid collide; if the projection point is located outside the two-dimensional convex hull, then calculating the shortest distance from the projection point to the two-dimensional convex hull and comparing the shortest distance with the radius of the cylinder; if the shortest distance is less than or equal to the radius of the cylinder, then determining that a collision has occurred, otherwise determining that no collision has occurred.

[0011] Further, the step of obtaining a set of feature points of the cuboid within the height range of the cylinder based on the transformed vertex coordinates of the cuboid and the height information of the cylinder includes: selecting vertices whose components perpendicular to the axis of the cylinder in the transformed vertex coordinates of the cuboid are within the height range of the cylinder as first-type feature points; calculating the coordinates of the intersection points of each edge of the cuboid with the planes containing the two bases of the cylinder, wherein each edge of the cuboid is formed by connecting two vertices in the transformed vertex coordinates of the cuboid, and taking all intersection coordinates as second-type feature points; and merging the first-type feature points and the second-type feature points to form the feature point set.

[0012] Furthermore, before transforming the cuboid to a cylindrical coordinate system centered on the cylinder, the method further includes: using the unit length axial vector of the cylinder as the first axial basis vector of the cylindrical coordinate system; calculating a first temporary vector perpendicular to the first axial basis vector based on the components of the unit length axial vector of the cylinder; performing a cross product operation between the first axial basis vector and the first temporary vector to obtain a second temporary vector perpendicular to both the first axial basis vector and the first temporary vector; normalizing the first temporary vector and the second temporary vector to obtain the second axial basis vector and the third axial basis vector of the cylindrical coordinate system; and constructing the cylindrical coordinate system based on the first axial basis vector, the second axial basis vector, and the third axial basis vector.

[0013] Further, the step of calculating a first temporary vector perpendicular to the first axial basis vector based on the components of the unit length axial vector of the cylinder includes: obtaining the three coordinate components of the unit length axial vector of the cylinder in the world coordinate system; constructing a temporary vector when the X-axis component and Y-axis component of the unit length axial vector are not simultaneously zero, wherein the X-axis component of the temporary vector is the negative of the Y-axis component of the unit length axial vector, the Y-axis component of the temporary vector is the X-axis component of the unit length axial vector, and the Z-axis component of the temporary vector is zero; and normalizing the temporary vector to obtain the first temporary vector.

[0014] Further, the step of projecting the set of feature points onto a plane perpendicular to the axis of the cylinder to form a two-dimensional projection point set, and constructing a two-dimensional convex hull based on the two-dimensional projection point set, includes: setting the component of each feature point in the set of feature points along the axis of the cylinder to zero, thereby obtaining a two-dimensional projection point on a plane perpendicular to the axis of the cylinder; and using the Graham scan algorithm to calculate the convex hull of the two-dimensional projection points, thereby obtaining the smallest convex polygon containing all the two-dimensional projection points as the two-dimensional convex hull.

[0015] Accordingly, a second aspect of the present invention provides an electronic device, including: at least one processor; and a memory connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the above-described cuboid and cylinder spatial collision detection method.

[0016] Accordingly, a third aspect of the present invention provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-described cuboid and cylinder spatial collision detection method.

[0017] The above-mentioned technical solutions of the embodiments of the present invention have the following beneficial technical effects: 1. By adopting a staged collision detection strategy, the projection axis method is first used for rapid elimination, which can efficiently complete the non-collision determination in most cases, greatly reducing the consumption of computing resources; only in a few complex cases where the projection axis method cannot determine the collision, the computationally intensive projection surface convex hull detection is used, thereby significantly improving the overall algorithm execution efficiency while ensuring detection accuracy, and meeting the strict requirements of robot control systems for real-time collision detection; 2. The four types of projection axis sets fully consider the geometric characteristics of both, and form a complete projection axis detection system by including multi-dimensional detection axes such as the cylinder axis, cuboid direction vector, cross product direction, and vertex perpendicular direction, which can cover most common collision situations, greatly improving the accuracy and reliability of preliminary screening, and avoiding the missed detection problem that may occur with a single projection axis detection method; 3. The projection convex hull detection method simplifies geometric relationships through coordinate system transformation, obtains a representative feature point set by using height interval filtering and edge section calculation, and then transforms the complex three-dimensional collision detection problem into efficient two-dimensional spatial calculation through two-dimensional convex hull construction and origin relationship determination. This method not only ensures the detection accuracy of complex collision scenarios, but also effectively controls the computational complexity, achieving the best balance between accuracy and efficiency. Attached Figure Description

[0018] Figure 1 is a schematic diagram of a cylinder provided in an embodiment of the present invention; Figure 2 is a schematic diagram of a cuboid provided in an embodiment of the present invention; Figure 3 is a flowchart of a spatial collision detection method between a cuboid and a cylinder provided in an embodiment of the present invention; Figure 4 is a schematic diagram of a preset projection axis set provided in an embodiment of the present invention; Figure 5 is a schematic diagram of projection surface convex hull detection provided in an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0020] First, as shown in Figure 1, the definition of a cylinder is as follows: The height of the cylinder The center of the cylinder Where is the radius of the cylinder. This is the axial vector per unit length of the cylinder.

[0021] set up and It is perpendicular to Two vectors, and A set of orthonormal bases is formed, and the parameterized expression for any point in the cylinder is as follows: (1) Among them, This represents any point inside the cylinder. Represents the coordinates of the cylinder's center. express and Length in direction, Indicates circling Angle of rotation for Length in direction, , , .

[0022] Secondly, as shown in Figure 2, the definition of a rectangle is as follows: B is the coordinate of the center of the cuboid, and L, W, and H are the length, width, and height, respectively. It is a unit orthogonal basis for the three directions of a cuboid.

[0023] The parameterized representation of any point within the cuboid is as follows: (2) Where R is the rotation matrix of the cuboid relative to the world coordinate system, It is a matrix formed by half the length, width, and height of a cuboid. Let be the coordinates of the i-th vertex.

[0024] Accordingly, the projection rules for a cuboid are as follows: Let 'a' be any unit vector in space, and the value of the line formed by projecting the 8 vertices of the cuboid onto this vector is: (3) The maximum and minimum values ​​of the rectangular prism projection on this projection axis are calculated as follows: (4) Accordingly, the projection rules for a cylinder are as follows: Let a be any unit vector in space, and the value of a point on the cylinder projected onto this vector is: (5) It can be seen from the above formula that when , and direction and When the directions are the same, take the maximum value. After substituting, the formula for the intermediate term is as follows: (6) Therefore, for any unit vector projection axis a, the maximum and minimum values ​​of the projection of any point of the cylinder onto that projection axis are as follows: (7) Referring to Figure 3, the first aspect of the present invention provides a spatial collision detection method for cuboid and cylinder, including the following steps: S100, based on a preset projection axis set, the projection range of cylinder and cuboid on each projection axis in the preset projection axis set is calculated by the projection axis method.

[0025] Based on a predefined set of projection axes, the projection axis method is used to calculate the projection intervals of the cylinder and cuboid on each projection axis. The projection axis set contains a total of fifteen projection axes in four categories: the first category is the unit axial vector of the cylinder; the second category is the three mutually orthogonal unit direction vectors of the cuboid; the third category is the three vectors obtained by the cross product of the cylinder's axial vector and the cuboid's direction vectors; and the fourth category is the eight direction vectors obtained by drawing perpendicular lines from the eight vertices of the cuboid to the cylinder's axis. For each projection axis, the projection interval of the cylinder on that axis and the extreme projection values ​​of the eight vertices of the cuboid on that axis are calculated, forming the projection interval of the cuboid.

[0026] Furthermore, the collision detection method for projection axes is as follows: for any projection axis formed by a unit vector 'a' in space, the projection range of the cylinder on that axis is... The projection range of the cuboid on this axis is For any projection axis a, if either of the following two equations is satisfied, it can be proven that the cylinder and the cuboid did not collide.

[0027] (8) Therefore, collision detection of cuboids and cylinders is simplified to finding the projection axis that can prove that the two have not collided.

[0028] S200, if there is at least one projection axis in the preset projection axis set that prevents the projection range of the cylinder from overlapping with the projection range of the cuboid, then it is determined that the cylinder and the cuboid have not collided.

[0029] By traversing all projection axes, if the projection regions of the cylinder and the cuboid on any projection axis do not overlap, it can be immediately determined that the two geometric objects have not collided. This criterion is based on the separating axis theorem; as long as there exists a projection axis that can separate the two objects, it can be ensured that the two objects do not interfere with each other in space. This fully utilizes the high computational efficiency of the projection axis method, enabling the determination of most non-collision cases in a very short time, significantly improving detection efficiency.

[0030] S300, if there is no projection axis in the preset projection axis set that prevents the projection range of the cylinder from overlapping with the projection range of the cuboid, then the projection surface convex hull detection is used to determine whether the cylinder and the cuboid collide.

[0031] When all projection axes fail to separate the two objects, convex hull detection is used for final determination. First, the vertices of the cuboid are transformed to a coordinate system centered on the cylinder. Then, the intersections of the cuboid vertices and their edges with the cylinder's base plane within the cylinder's height range are collected, forming a set of feature points. These feature points are projected onto a plane perpendicular to the cylinder's axis, and a two-dimensional convex hull is constructed using the Graham scan algorithm. Finally, the collision state is determined by judging the positional relationship between the projected points on the cylinder's axis and the convex hull (the point is inside the convex hull or the shortest distance from the point to the convex hull is less than or equal to the cylinder's radius).

[0032] By employing a phased detection strategy, the algorithm first utilizes the computationally efficient projection axis method to quickly eliminate most non-collision cases. Only when necessary is the computationally intensive but more accurate projection surface convex hull detection enabled. This approach ensures the reliability of collision detection while significantly improving the overall execution efficiency of the algorithm. The pre-defined set of projection axes fully considers the spatial characteristics of both geometries, effectively covering common relative configurations. The secondary detection method based on coordinate system transformation and convex hull analysis ensures accuracy in complex contact situations. This method is particularly suitable for applications requiring high real-time performance, such as robot motion planning and virtual simulation.

[0033] Specifically, please refer to Figure 4. The preset projection axis set includes: a first projection axis subset, a second projection axis subset, a third projection axis subset, and a fourth projection axis subset.

[0034] The first projection axis subset includes the axial vector of the cylinder per unit length. This axial vector defines the cylinder's primary extension direction. By projecting two geometric bodies onto this axis, potential overlap along the cylinder's axial direction can be effectively detected. This is the key detection direction for determining whether two geometric bodies are interfering axially.

[0035] The second projection axis subset comprises three mutually orthogonal unit direction vectors of the cuboid. These vectors fully define the spatial orientation of the cuboid, corresponding to its length, width, and height. By performing projection interval detection along these three directions, all major spatial relationships within the cuboid's own coordinate system can be comprehensively covered, ensuring effective detection of collisions under various poses of the cuboid.

[0036] The third projection axis subset comprises three vectors obtained by performing a cross product operation between the cylinder's axial vector and each unit direction vector of the cuboid. These three newly generated vectors are perpendicular to the planes defined by the cylinder's axial direction and the cuboid's direction vectors, providing the ability to detect the relative positions of two geometric objects in oblique directions. These projection axes can capture potential collisions that do not occur along the main coordinate axes, greatly enhancing the completeness of the detection.

[0037] The fourth projection axis subset comprises several direction vectors determined by drawing perpendicular lines from multiple vertices of the cuboid to the axis of the cylinder. These vectors represent the shortest distance directions from each feature point of the cuboid to the axis of the cylinder, effectively detecting complex spatial relationships between the vertices of the cuboid and the sides of the cylinder. Particularly when the cuboid approaches the cylinder at a specific angle, these projection axes provide crucial separation and detection capabilities.

[0038] By using the four subsets of projection axes described above, a multi-dimensional, multi-directional projection axis detection system can be established. These projection axes fully consider the spatial characteristics of both cylinders and cuboids, as well as their various possible relative configurations, providing effective separation detection in different directions. The first type of axis addresses the axial characteristics of cylinders, the second type covers the body direction of cuboids, the third type detects the relative position in oblique directions, and the fourth type handles the complex spatial relationships between vertices and sides. This comprehensive projection axis design ensures that the separation state of two geometries can be detected quickly and accurately in most cases, providing an efficient preliminary screening mechanism for potentially more precise subsequent detection.

[0039] The collision rules for cuboids and cylinders are as follows: A cuboid is characterized by points, lines, and faces. A cylinder is characterized by its base, rings, and walls. The base consists of the two bottom faces of the cylinder, the ring represents the circle formed by the boundaries of the two bottom faces, and the walls are the lateral faces of the cylinder. All possible collisions between a cuboid and a cylinder, along with their corresponding detectable projection axes, are shown in the table below: As shown in the table above, the projection axis proposed in this invention can determine most cases. However, in the case of collision between a line and a loop, no projection axis can be found. Therefore, in this case, this invention proposes a projection surface convex hull detection method.

[0040] Specifically, step S300, which uses projection surface convex hull detection to determine whether the cylinder and the cuboid collide, includes: S310, transforming the cuboid into a cylindrical coordinate system established with the cylinder as the center, and obtaining the coordinates of the transformed cuboid vertices.

[0041] The cuboid is transformed into a cylindrical coordinate system centered at the cylinder, yielding the coordinates of its vertices. First, a local coordinate system is established with the cylinder's center as the origin and its axis as the Z-axis. Coordinate transformation is then performed to convert the coordinates of all vertices of the cuboid to this system. This transformation includes translation and rotation operations. Translation moves the origin of the coordinate system to the center of the cylinder, while rotation aligns the Z-axis of the coordinate system with the cylinder's axis, simplifying subsequent calculations.

[0042] S320: Based on the transformed vertex coordinates of the cuboid and the height information of the cylinder, obtain the set of feature points of the cuboid within the height range of the cylinder.

[0043] Based on the transformed vertex coordinates of the cuboid and the height information of the cylinder, a set of feature points of the cuboid within the height range of the cylinder is obtained. Two types of feature points are collected: first, the original vertices of the cuboid whose transformed Z-coordinates fall within the height range of the cylinder; second, the coordinates of the intersection points of each edge of the cuboid with the planes containing the top and bottom faces of the cylinder. By calculating the intersection points of the edges with the planes, it is ensured that edge features that partially cross the height range of the cylinder are captured.

[0044] S330: Project the set of feature points onto a plane perpendicular to the axis of the cylinder to form a two-dimensional projection point set, and construct a two-dimensional convex hull based on the two-dimensional projection point set.

[0045] The set of feature points is projected onto a plane perpendicular to the axis of the cylinder, forming a two-dimensional projected point set. A two-dimensional convex hull is then constructed based on this point set. The Z-coordinate components of all feature points are set to zero, and they are projected onto the XY plane to obtain a two-dimensional point set. Subsequently, the Graham scan algorithm is used to calculate the convex hull of these points, generating the smallest convex polygon containing all feature points.

[0046] S340: Based on the position and distance relationship between the projection point of the cylinder's central axis and the two-dimensional convex hull, determine whether the cylinder and the cuboid collide.

[0047] Based on the position and distance relationship between the projection point of the cylinder's central axis and the two-dimensional convex hull, it is determined whether the cylinder and the cuboid collide. First, it is determined whether the origin (i.e., the projection point of the cylinder's axis) is located inside the convex hull. If it is inside, a collision is determined; if it is outside, the shortest distance from the origin to the convex hull is calculated. If this distance is less than or equal to the cylinder's radius, a collision is determined; otherwise, no collision is determined.

[0048] By establishing a local coordinate system for the cylinder, the geometric relationships are simplified, and coordinate transformation transforms the 3D collision detection problem into a geometric relationship judgment within a 2D plane. By collecting feature points of the cuboid within the height range of the cylinder and constructing a convex hull, the spatial relative positional relationship between the cuboid and the cylinder can be accurately described. Employing convex hull analysis and distance calculation ensures the accuracy of the collision detection results, exhibiting particularly good reliability when handling complex spatial relationships. While maintaining detection accuracy, dimensionality reduction significantly reduces computational complexity, making it suitable for engineering applications with high real-time requirements.

[0049] Further, in step S340, determining whether the cylinder and the cuboid collide based on the position and distance relationship between the projection point of the cylinder's central axis and the two-dimensional convex hull includes: S341, determining whether the projection point of the cylinder's central axis is located inside the two-dimensional convex hull.

[0050] To determine whether the projection point of the central axis of a cylinder lies inside the two-dimensional convex hull, the positional relationship between the projection point and the convex polygon is calculated. Computational geometry methods such as the ray casting method or the wrap-around number algorithm are employed to accurately determine whether the cylinder is inside the convex hull by analyzing the positional relationship between the projection point and each side of the convex hull. This determination is based on the geometric property that the convex hull completely represents the cross-sectional shape of the cuboid within the height range of the cylinder.

[0051] S342, if the projection point is located inside the two-dimensional convex hull, then it is determined that the cylinder and the cuboid have collided.

[0052] If the projection point is located inside the two-dimensional convex hull, then the cylinder and the cuboid are determined to have collided. This determination is based on the following geometric fact: when the projection point of the cylinder's central axis is located inside the convex hull, it indicates that the central axis of the cylinder passes through the solid region of the cuboid. At this time, regardless of the size of the cylinder's radius, the two geometric bodies must have a spatial overlap, so a collision conclusion can be directly drawn.

[0053] S343, if the projection point is located outside the two-dimensional convex hull, calculate the shortest distance from the projection point to the two-dimensional convex hull and compare the shortest distance with the radius of the cylinder.

[0054] If the projection point is located outside the 2D convex hull, the shortest distance from the projection point to the convex hull is calculated and compared with the radius of the cylinder. A nearest-point search algorithm is used to determine the shortest distance between the projection point and each edge of the convex hull by calculating the minimum distance from the projection point to each edge. This calculation process needs to consider the perpendicular distance from the projection point to the lines containing each edge of the convex hull and determine whether the foot of the perpendicular is within the range of the edge segment.

[0055] S344: If the shortest distance is less than or equal to the radius of the cylinder, a collision is determined to have occurred; otherwise, no collision is determined to have occurred.

[0056] If the shortest distance is less than or equal to the radius of the cylinder, a collision is considered to have occurred; otherwise, no collision is considered to have occurred. This criterion is based on the following principle: when the shortest distance from the projection point to the convex hull does not exceed the radius of the cylinder, it indicates that the cylindrical region centered on the cylinder's central axis and encompassing its radius intersects with the cuboid; conversely, when the shortest distance is greater than the cylinder's radius, it ensures that the two geometric bodies are completely separated in space.

[0057] A complete collision detection judgment system was established through systematic positional relationship judgment and distance calculation. First, a preliminary judgment is made based on the relative positional relationship between the projection point and the convex hull. When a direct judgment is not possible, precise distance parameters are calculated, and a definitive conclusion is reached based on distance comparison. This method fully utilizes the geometric properties of the convex hull, transforming the complex 3D collision problem into precise 2D geometric calculations, ensuring both the accuracy of the judgment results and maintaining low computational complexity. In particular, through a hierarchical judgment strategy, simple positional relationship judgments are prioritized, while relatively complex distance calculations are performed only when necessary, effectively balancing the algorithm's efficiency and accuracy requirements, making it particularly suitable for engineering fields requiring real-time collision detection.

[0058] Furthermore, since the orthonormal basis u, uv, and w of the cylinder satisfy pairwise perpendicularity, expressions for u and v can be easily found, and the expression for the cylinder axis w is: For ease of calculation, the expressions for u and v are as follows: (9) From this, we can further derive the rotation matrix of the cylinder as follows: To simplify the calculation, the cuboid needs to be transformed into a coordinate system with the cylinder's center as the origin. Since the projection process only requires projecting onto each vertex, the transformation is performed only on each vertex. Let the coordinates of the i-th vertex after the transformation be denoted as . Its expression is: (10) Where C is the center coordinate of the original cylinder. After the transformation, the center coordinate of the cylinder is converted to , axis vector .

[0059] After transforming to a cylindrical coordinate system, the projection of any point in this space onto the cylinder's axis depends only on the point's z-axis value, simplifying the projection process. Furthermore, the cylinder's height divides the projection interval into three parts, respectively... .

[0060] Next, we need to calculate the vertices of the convex polyhedron formed by the two sets of planes formed by the top and bottom faces of the cylinder cutting the cuboid. The cuboid has 12 edges, and the endpoints of each edge are formed by two vertices of the cuboid. Let's denote the vertices... and For the two endpoints that form the sides of the cuboid ( It is easy to see that when the projection values ​​of the two vertices on the axis of the cylinder are not in the same part, the line segment will be cut. Based on the proportion of the line segment being cut, the point where the line segment is cut can be calculated. In this way, the vertices of the 12 edges cut by the plane can be calculated and stored in the set G.

[0061] Following the steps above, continue calculating the projection values ​​of the eight vertices of the cuboid onto the axis of the cylinder. When the projection values ​​are within the interval... When the vertex is in the set G, store it in the set G.

[0062] At that time, the coordinates of vertices that satisfy the projection values ​​and the coordinates of the cut convex polygons have been stored in the set G. The z-value of the coordinate points in the set is set to 0, forming a series of scattered points in the two-dimensional plane.

[0063] The Graham Scan algorithm is used to calculate the convex hull formed by these scattered points. There are two cases: one is that the origin is inside the convex hull, in which case the cuboid and the cylinder collide; the other is that the origin is outside the convex hull, the shortest distance dis from the origin to the convex hull is calculated, and if dis ≤ r, the cylinder and the cuboid collide, as shown in Figure 5.

[0064] Further, in step S320, based on the transformed cuboid vertex coordinates and the cylinder height information, a set of feature points of the cuboid within the cylinder height range is obtained, including: S321, selecting vertices whose components of the transformed cuboid vertex coordinates perpendicular to the cylinder axis are within the cylinder height range as the first type of feature points.

[0065] Vertices whose coordinate components perpendicular to the cylinder axis in the transformed cuboid's coordinate system fall within the cylinder's height range are selected as the first type of feature points. Building upon the coordinate system transformation, this step further filters vertices by examining their Z-coordinate components along the cylinder axis, identifying those with Z-coordinate values ​​between -1 / 2 and -1 / 2 of the cylinder's height. These vertices are directly located within the cylinder's height space, effectively representing the cuboid's spatial occupancy within this region and providing fundamental geometric data for subsequent collision detection.

[0066] S322, calculate the coordinates of the intersection points of each edge of the cuboid with the plane containing the two bases of the cylinder. Each edge of the cuboid is formed by connecting two vertices in the transformed cuboid vertex coordinates, and all intersection point coordinates are used as the second type of feature points.

[0067] The coordinates of the intersection points of each edge of the cuboid with the plane containing the two bases of the cylinder are calculated. Each edge of the cuboid is formed by connecting two vertices from the transformed cuboid vertex coordinates, and all intersection point coordinates are used as second-type feature points. This step iterates through all twelve edges of the cuboid. For each edge, it is determined whether the Z coordinates of its two endpoints lie on opposite sides of the plane containing the top and bottom bases of the cylinder. When such edges exist, the coordinates of the intersection points between the edges and the planes are accurately calculated using linear interpolation. These intersection points represent the key locations where the height boundaries of the cuboid and cylinder intersect, ensuring that the set of feature points can completely describe the cross-sectional shape of the cuboid within the height range of the cylinder.

[0068] S323, merge the first type of feature points with the second type of feature points to form a feature point set.

[0069] The first and second types of feature points are merged to form a feature point set. This step integrates all feature points obtained in the first two steps into a unified set, including all original vertices that meet the conditions and the intersection points of edges that intersect with the base of the cylinder. This complete feature point set accurately describes the cross-sectional profile of the cuboid within the height range of the cylinder, providing a comprehensive geometric information foundation for subsequent 2D projection and convex hull construction.

[0070] A systematic feature point collection method ensures the accuracy and completeness of collision detection. First, original vertices within the cylinder's height range are collected, preserving the basic geometric features of the cuboid. Second, by calculating the intersections of edges and the base, geometric features partially traversing the cylinder's height range are captured. Finally, the two types of feature points are merged to form a complete set. This method fully considers the various possible spatial relative positions of the cuboid and cylinder, especially handling the case where the cuboid partially traverses the cylinder's height range, ensuring that the feature point set accurately reflects the relationship between the two geometric shapes in three-dimensional space. This refined feature point collection strategy provides a reliable geometric data foundation for subsequent collision determination, guaranteeing the accuracy of the detection results while avoiding unnecessary computational overhead.

[0071] Furthermore, before transforming the cuboid to a cylindrical coordinate system centered on the cylinder in step S310, the method further includes: S301, using the axial vector of the cylinder per unit length as the first axial basis vector of the cylindrical coordinate system.

[0072] First, the core reference direction of the cylindrical coordinate system is determined, namely, the axial vector of the cylinder itself is used as the Z-axis reference direction of the coordinate system. This axial vector not only defines the main extension direction of the cylinder, but also provides the primary reference for establishing a complete local coordinate system, ensuring the consistency between the subsequent coordinate system construction and the actual spatial orientation of the cylinder.

[0073] S302, calculate the first temporary vector perpendicular to the first axial basis vector based on the components of the axial vector per unit length of the cylinder.

[0074] By analyzing the components of the axial vector in the world coordinate system, a temporary vector orthogonal to the axial vector is generated using a geometric construction method. Specifically, when the X and Y components of the axial vector are not simultaneously zero, a new vector is constructed by swapping and inverting the components. This new vector ensures that it remains perpendicular to the original axial vector, laying the foundation for building a complete orthogonal coordinate system.

[0075] S303, perform a cross product operation between the first axial basis vector and the first temporary vector to obtain a second temporary vector that is perpendicular to both the first axial basis vector and the first temporary vector.

[0076] By utilizing the mathematical properties of the cross product of vectors, a third vector orthogonal to it can be calculated from two known mutually perpendicular vectors. This operation ensures the pairwise perpendicularity between the three vectors, forming a complete set of orthogonal vectors in space, providing the necessary mathematical foundation for constructing a standard orthogonal coordinate system.

[0077] S304, normalize the first temporary vector and the second temporary vector respectively to obtain the second axial basis vector and the third axial basis vector of the cylindrical coordinate system.

[0078] The two temporary vectors are normalized to become unit-length vectors. By calculating the magnitude of each vector and dividing each component by that magnitude, the resulting basis vectors are ensured to not only maintain orthogonality but also have unit length, thus forming an orthonormal basis that satisfies the mathematical requirements for coordinate system construction.

[0079] S305, a cylindrical coordinate system is constructed based on the first axial basis vector, the second axial basis vector, and the third axial basis vector.

[0080] We establish a local Cartesian coordinate system with the center of the cylinder as the origin by using three mutually orthogonal unit vectors as the coordinate axis basis vectors. The first axial basis vector defines the Z-axis direction, and the second and third axial basis vectors define the X-axis and Y-axis directions, respectively, forming a complete right-handed coordinate system that provides an accurate mathematical reference framework for subsequent geometric transformations and calculations.

[0081] A systematic coordinate system construction method was employed to establish a local coordinate system that perfectly matches the spatial orientation of the cylinder. Based on the cylinder's inherent geometric properties, this coordinate system ensures orthogonality and normalization of the coordinate axes through rigorous mathematical calculations. This coordinate system construction method not only accurately reflects the cylinder's actual spatial orientation but, more importantly, simplifies and optimizes subsequent collision detection calculations. By transforming the vertices of the cuboid to this local coordinate system, complex three-dimensional spatial relationships can be transformed into relatively simple calculations. This is particularly effective when dealing with geometric relationships within the cylinder's height range, significantly reducing computational complexity, improving detection efficiency, and ensuring the accuracy and reliability of the calculation results.

[0082] Further, in step S302, the first temporary vector perpendicular to the first axial basis vector is calculated based on the components of the axial vector per unit length of the cylinder, including: S3021, obtaining the three coordinate components of the axial vector per unit length of the cylinder in the world coordinate system.

[0083] First, the mathematical representation of the cylinder's axial vector in the original world coordinate system is read, and its component values ​​in the X, Y, and Z axes are extracted. These component values ​​accurately represent the vector's direction in three-dimensional space as floating-point numbers, providing an accurate numerical basis for subsequent calculations. By obtaining this fundamental data, it is ensured that all subsequent calculations are based on accurate spatial geometric relationships.

[0084] S3022, when the X-axis component and Y-axis component of the unit length axial vector are not simultaneously zero, construct a temporary vector. The X-axis component of the temporary vector is the negative of the Y-axis component of the unit length axial vector, the Y-axis component of the temporary vector is the X-axis component of the unit length axial vector, and the Z-axis component of the temporary vector is zero.

[0085] A specific vector construction algorithm is employed to generate a new vector orthogonal to the original axial vector by swapping the X and Y components of the axial vector and inverting one of the components. This construction method is based on the mathematical principle of vector orthogonality, ensuring that the dot product of the newly generated temporary vector and the original axial vector is zero, thus satisfying the geometric orthogonality condition. When the axial vector is close to the Z-axis, this method effectively avoids numerical instability problems.

[0086] S3023, normalize the temporary vector to obtain the first temporary vector.

[0087] The magnitude of the temporary vector is calculated, which is the square root of the sum of the squares of its components. Then, each component is divided by this magnitude to obtain a unit vector of length 1. This normalization process ensures the accuracy of subsequent coordinate system construction, making the obtained basis vectors both orthogonal to the axial vectors and possessing a standard unit length, thus laying the foundation for constructing an orthogonal normalized coordinate system.

[0088] A systematic vector processing procedure was adopted to accurately calculate the basis vectors perpendicular to the cylinder's axis. First, the spatial components of the axial vector were obtained. Then, temporary vectors were constructed based on the principle of vector orthogonality. Finally, normalization was performed to obtain the standardized basis vectors. This method fully considers the numerical stability of vector calculations, exhibiting particularly good robustness when handling vectors with special directions. Rigorous mathematical calculations and a standardized processing procedure ensure that the generated basis vectors not only remain strictly perpendicular to the cylinder's axis but also possess unit length characteristics, providing an accurate mathematical foundation for subsequent coordinate system transformations and collision detection calculations. This basis vector generation method is computationally efficient, numerically stable, and adaptable to cylinders with various spatial postures, providing crucial assurance for the reliability and accuracy of the entire collision detection algorithm.

[0089] Further, step S330 involves projecting the set of feature points onto a plane perpendicular to the axis of the cylinder to form a two-dimensional projection point set, and constructing a two-dimensional convex hull based on the two-dimensional projection point set. This includes: S331, setting the component of each feature point in the set of feature points along the axis of the cylinder to zero, thereby obtaining a two-dimensional projection point on a plane perpendicular to the axis of the cylinder.

[0090] By eliminating the coordinate components of all feature points along the cylinder's axis, the feature points in three-dimensional space are projected onto a two-dimensional plane perpendicular to the cylinder's axis. This projection operation preserves the relative positional relationships of the feature points on the plane perpendicular to the axis, while simplifying the problem from three-dimensional space to a two-dimensional plane, laying the foundation for subsequent convex hull calculation. After projection, each feature point retains only its coordinate components in two horizontal directions, forming a two-dimensional coordinate point set that accurately reflects the distribution of the original feature points on the plane perpendicular to the cylinder's axis.

[0091] S332 uses the Graham scan algorithm to calculate the convex hull of the two-dimensional projection points, and obtains the smallest convex polygon containing all the two-dimensional projection points as the two-dimensional convex hull.

[0092] First, the 2D point set is preprocessed by finding the pole as the starting point, and then sorting the remaining points according to their polar angles. The sorted point set is then traversed sequentially, and the orientation relationships of the points are determined using the cross product of vectors, gradually constructing the convex hull boundary. This method efficiently calculates the smallest convex polygon containing all points, accurately describing the outer contour shape of the point set. The final convex hull is a series of sequentially connected polygon vertices, completely containing all 2D projection points, providing accurate geometric boundary information for subsequent collision detection.

[0093] By projecting 3D feature points onto a 2D plane and constructing a convex hull, the dimensionality of the collision detection problem is simplified. The projection operation preserves the necessary geometric relationships, while the convex hull calculation accurately captures the distribution characteristics of the feature point set. The Graham scan algorithm ensures the efficiency and accuracy of the convex hull calculation; this algorithm has low time complexity and can quickly process a large number of feature points. This method transforms the complex 3D collision detection problem into a geometric relationship judgment within a 2D plane, significantly reducing computational complexity while ensuring the accuracy of the detection results. The compact geometric representation of the convex hull not only reduces the amount of data required for subsequent calculations but also provides clear geometric boundary information, making collision determination more intuitive and efficient, particularly suitable for engineering applications requiring real-time processing.

[0094] Accordingly, a second aspect of the present invention provides an electronic device, including: at least one processor; and a memory connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the above-described cuboid and cylinder spatial collision detection method.

[0095] Accordingly, a third aspect of the present invention provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-described cuboid and cylinder spatial collision detection method.

[0096] This invention aims to protect a method for detecting collisions between cuboids and cylinders in space, which has the following advantages: 1. By adopting a staged collision detection strategy, the projection axis method is first used for rapid elimination, which can efficiently complete the non-collision determination in most cases, greatly reducing the consumption of computing resources; only in a few complex cases where the projection axis method cannot determine the collision, the computationally intensive projection surface convex hull detection is used, thereby significantly improving the overall algorithm's execution efficiency while ensuring detection accuracy, meeting the stringent requirements of robot control systems for real-time collision detection; 2. The four types of projection axis sets fully consider the geometric characteristics of both objects, forming a complete projection axis detection system by including multi-dimensional detection axes such as the cylinder axis, cuboid direction vector, cross product direction, and vertex perpendicular direction, which can cover most common collision situations, greatly improving the accuracy and reliability of the initial screening, and avoiding the missed detection problem that may occur with a single projection axis detection method; 3. The projection convex hull detection method simplifies geometric relationships through coordinate system transformation, obtains a representative feature point set by using height interval filtering and edge section calculation, and then transforms the complex three-dimensional collision detection problem into efficient two-dimensional spatial calculation through two-dimensional convex hull construction and origin relationship determination. This method not only ensures the detection accuracy of complex collision scenarios, but also effectively controls the computational complexity, achieving the best balance between accuracy and efficiency.

[0097] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0098] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in one or more blocks of the flowchart illustrations and / or one or more blocks of the block diagrams.

[0099] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more flowcharts and / or one or more block diagrams.

[0100] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, such that the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions specified in one or more flowcharts and / or one or more block diagrams.

[0101] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for detecting spatial collisions between a cuboid and a cylinder, characterized in that, The process includes the following steps: Based on a preset set of projection axes, the projection axis method is used to calculate the projection intervals of the cylinder and the cuboid on each projection axis in the preset set of projection axes; if there is at least one projection axis in the preset set of projection axes that prevents the projection intervals of the cylinder and the cuboid from overlapping, it is determined that the cylinder and the cuboid have not collided; if there is no projection axis in the preset set of projection axes that prevents the projection intervals of the cylinder and the cuboid from overlapping, the projection surface convex hull detection is used to determine whether the cylinder and the cuboid have collided.

2. The method for detecting spatial collisions between a cuboid and a cylinder according to claim 1, characterized in that, The preset projection axis set includes: a first projection axis subset, a second projection axis subset, a third projection axis subset, and a fourth projection axis subset; the first projection axis subset includes the axial vector of the cylinder per unit length; the second projection axis subset includes three mutually orthogonal unit direction vectors of the cuboid; the third projection axis subset includes three vectors obtained by performing a cross product operation between the axial vector of the cylinder and each of the unit direction vectors of the cuboid; the fourth projection axis subset includes several direction vectors determined by drawing perpendicular lines from multiple vertices of the cuboid to the axis of the cylinder.

3. The method for detecting spatial collisions between a cuboid and a cylinder according to claim 1 or 2, characterized in that, The step of using projection plane convex hull detection to determine whether the cylinder and the cuboid collide includes: transforming the cuboid into a cylindrical coordinate system centered on the cylinder to obtain the coordinates of the transformed cuboid vertices; based on the transformed cuboid vertices coordinates and the height information of the cylinder, obtaining a set of feature points of the cuboid within the height range of the cylinder; projecting the set of feature points onto a plane perpendicular to the axis of the cylinder to form a two-dimensional projection point set; constructing a two-dimensional convex hull based on the two-dimensional projection point set; and determining whether the cylinder and the cuboid collide based on the position and distance relationship between the projection points of the cylinder's central axis and the two-dimensional convex hull.

4. The spatial collision detection method for cuboids and cylinders according to claim 3, characterized in that, The step of determining whether the cylinder and the cuboid collide based on the position and distance relationship between the projection point of the cylinder's central axis and the two-dimensional convex hull includes: determining whether the projection point of the cylinder's central axis is located inside the two-dimensional convex hull; if the projection point is located inside the two-dimensional convex hull, then determining that the cylinder and the cuboid collide; if the projection point is located outside the two-dimensional convex hull, then calculating the shortest distance from the projection point to the two-dimensional convex hull and comparing the shortest distance with the radius of the cylinder; if the shortest distance is less than or equal to the radius of the cylinder, then determining that a collision has occurred, otherwise determining that no collision has occurred.

5. The method for detecting spatial collisions between a cuboid and a cylinder according to claim 3, characterized in that, The step of obtaining a set of feature points of the cuboid within the height range of the cylinder based on the transformed vertex coordinates of the cuboid and the height information of the cylinder includes: selecting vertices whose components perpendicular to the axis of the cylinder in the transformed vertex coordinates are within the height range of the cylinder as first-type feature points; calculating the coordinates of the intersection points of each edge of the cuboid with the plane containing the two bases of the cylinder, wherein each edge of the cuboid is formed by connecting two vertices in the transformed vertex coordinates of the cuboid, and taking all intersection coordinates as second-type feature points; and merging the first-type feature points and the second-type feature points to form the feature point set.

6. The method for detecting spatial collisions between a cuboid and a cylinder according to claim 3, characterized in that, Before transforming the cuboid to a cylindrical coordinate system centered on the cylinder, the method further includes: using the unit length axial vector of the cylinder as the first axial basis vector of the cylindrical coordinate system; calculating a first temporary vector perpendicular to the first axial basis vector based on the components of the unit length axial vector of the cylinder; performing a cross product operation between the first axial basis vector and the first temporary vector to obtain a second temporary vector perpendicular to both the first axial basis vector and the first temporary vector; normalizing the first temporary vector and the second temporary vector to obtain the second axial basis vector and the third axial basis vector of the cylindrical coordinate system; and constructing the cylindrical coordinate system based on the first axial basis vector, the second axial basis vector, and the third axial basis vector.

7. The method for detecting spatial collisions between a cuboid and a cylinder according to claim 6, characterized in that, The step of calculating a first temporary vector perpendicular to the first axial basis vector based on the components of the axial vector per unit length of the cylinder includes: obtaining the three coordinate components of the axial vector per unit length of the cylinder in the world coordinate system; constructing a temporary vector when the X-axis component and Y-axis component of the axial vector per unit length are not simultaneously zero, wherein the X-axis component of the temporary vector is the negative of the Y-axis component of the axial vector per unit length, the Y-axis component of the temporary vector is the X-axis component of the axial vector per unit length, and the Z-axis component of the temporary vector is zero; and normalizing the temporary vector to obtain the first temporary vector.

8. The method for detecting spatial collisions between a cuboid and a cylinder according to claim 3, characterized in that, The step of projecting the set of feature points onto a plane perpendicular to the axis of the cylinder to form a two-dimensional projection point set, and constructing a two-dimensional convex hull based on the two-dimensional projection point set, includes: setting the component of each feature point in the set of feature points along the axis of the cylinder to zero, thereby obtaining a two-dimensional projection point on a plane perpendicular to the axis of the cylinder; and using the Graham scan algorithm to calculate the convex hull of the two-dimensional projection points, thereby obtaining the smallest convex polygon containing all the two-dimensional projection points as the two-dimensional convex hull.

9. An electronic device, characterized in that, include: At least one processor; The at least one processor is connected to a memory; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the cuboid and cylinder spatial collision detection method as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, It stores computer instructions, which, when executed by a processor, implement the cuboid and cylinder spatial collision detection method as described in any one of claims 1-8.

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