Examining the use of B-splines in parking assist systems

The main objective of the presented study and simulations conducted was to investigate the prospect of using B-spline curves for the automatic parking, i.e. self-driving, or intelligent vehicles. We consider the problem of parallel parking for a non-holonomic vehicle with a known maximum path curvature. The relationship between the properties of the path and the geometry of corresponding parking spot is revealed. The unique properties of B-splines are exploited to synthesize a path that is smooth and of continuous curvature. The contributions of this project are in the generations of better, smooth continuous paths. This improves passenger comfort during the parallel parking maneuver and allow vehicles to park in tighter spots by increasing the feasible range of the parking manoeuver

Kvadratni splajnovi, po dijelovima bez kolizija, s regularnim kvadratnim barijerama

We classify mutual position of a quadratic Bézier curve and a regular quadric in three dimensional Euclidean space. For given first and last control point, we find the set of all quadratic Bezier curves having no common point with a regular quadric. This system of such quadratic Bézier curves is represented by the set of their admissible middle control points. The spatial problem is reduced to a planar problem where the regular quadric is represented by a conic section. Then, the set of all middle control points is found for each type of conic section separately. The key issue is to find the boundary of this set. It is formed from the middle control points of the Bézier curves touching the given conic section. Our results are applicable in collision-free paths computation for virtual agents where the obstacles are represented or bounded by regular quadrics. Another application can be found in searching for pointwise space-like curves in Minkowski space.U trodimenzionalnom euklidskom prostoru klasiciramo međusobni odnos kvadratne Bézierove krivulje i regularne kvadrike. Za danu prvu i zadnju kontrolnu točku, nalazimo skup svih kvadratnih Bézierovih krivulja koje nemaju zajedničku točku s regularnom kvadrikom. Sustav ovakvih kvadratnih Bézierovih krivulja prikazuje se skupom njihovih dopustivih srednjih kontrolnih točaka. Prostorni problem svodi se na ravninski problem gdje konika predstavlja regularnu kvadriku. Tada se za svaku vrstu konike zasebno nalazi skup svih srednjih kontrolnih točaka. Glavna zadaća je naći granicu ovakvog skupa. Spomenutu granicu čine središnje kontrolne točke Bézierovih krivulja koje diraju koniku. Naši rezultati primjenjuju se u računanju putanja bez kolizija za virtualna sredstva gdje su barijere prikazane ili ograničene regularnim kvadrikama. Drugu primjenu nalazimo u istrazivanju točkovnih prostornih krivulja u prostoru Minkowski