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Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.
It is the locus corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity. Equivalently, in polar coordinates ( r , θ ) it can be described by the equation r = b ⋅ θ {\displaystyle r=b\cdot \theta } with real number b .
The instant center is the point in the moving plane around which all other points are rotating at a specific instant of time. The continuous movement of a plane has an instant center for every value of the time parameter. This generates a curve called the moving centrode. The points in the fixed plane corresponding to these instant centers form ...
The indigo dot draws both centrodes, and also indicates where the moving centrode is in contact with and is rolling around the fixed centrode. A centrode, in kinematics, is the path traced by the instantaneous center of rotation of a rigid plane figure moving in a plane. There are two types of centrodes: a space or fixed centrode, and a body or ...
Cut locus C(P) of a point P on the surface of a cylinder. A point Q in the cut locus is shown with two distinct shortest paths , connecting it to P.. In the Euclidean plane, a point p has an empty cut locus, because every other point is connected to p by a unique geodesic (the line segment between the points).
These show the direction in which a massless fluid element will travel at any point in time. [3] Streaklines are the loci of points of all the fluid particles that have passed continuously through a particular spatial point in the past. Dye steadily injected into the fluid at a fixed point (as in dye tracing) extends along a streakline.
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In mathematics, a generalized conic is a geometrical object defined by a property which is a generalization of some defining property of the classical conic.For example, in elementary geometry, an ellipse can be defined as the locus of a point which moves in a plane such that the sum of its distances from two fixed points – the foci – in the plane is a constant.