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In applied mathematics, an Akima spline is a type of non-smoothing spline that gives good fits to curves where the second derivative is rapidly varying. [1] The Akima spline was published by Hiroshi Akima in 1970 from Akima's pursuit of a cubic spline curve that would appear more natural and smooth, akin to an intuitively hand-drawn curve.
Simulink is a MATLAB-based graphical programming environment for modeling, simulating and analyzing multidomain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block libraries .
Two intersecting lines. In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line.Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection.
Given a function : (i.e. from the real numbers to the real numbers), we can decide if it is injective by looking at horizontal lines that intersect the function's graph. If any horizontal line = intersects the graph in more than one point, the function is not injective. To see this, note that the points of intersection have the same y-value ...
Stateflow is generally used to specify the discrete controller in the model of a hybrid system where the continuous dynamics (i.e., the behavior of the plant and environment) are specified using Simulink. [4] [5] Specific applications for Stateflow include: Mode logic, where each discrete mode of a system is represented by a state [6]
No intersection at all; Intersection in exactly one point; Intersection in two points. Methods for distinguishing these cases, and determining the coordinates for the points in the latter cases, are useful in a number of circumstances. For example, it is a common calculation to perform during ray tracing. [1]
First, find out if the line produced by the ray intersects with the plane that the triangle is on, and if it does, find the coordinates of that intersection. The only way that the line will not intersect the plane is if the ray's direction vector is parallel to the plane. [ 3 ]
The Shamos–Hoey algorithm [1] applies this principle to solve the line segment intersection detection problem, as stated above, of determining whether or not a set of line segments has an intersection; the Bentley–Ottmann algorithm works by the same principle to list all intersections in logarithmic time per intersection.