s2mc-client-core/io.github.kory33.s2mctest.core.client.api/DiscretePath

DiscretePath

class DiscretePath[V, F](val points: Vector[V])(using nvs: NormedVectorSpace[V, F], order: Order[F])

Class of discrete path on a normed vector space V which consists of points in V of positive number. These objects, unlike continuous (with respect to the metric induced by norm on V) paths represented by [0, 1] -> V, has lost information on how fast these points should be traversed.

V must be a normed vector space over an ordered field F, which should be a subfield of the set of real numbers. It is required that the field operations are compatible with order relations. For more details, see https://en.wikipedia.org/w/index.php?title=Ordered_field&oldid=1049796158#Definitions.

Value Params

points: a nonempty sequence of points of V

Companion

object

class Object

trait Matchable

class Any

Value members

Concrete methods

Concatenate another path. The last point of this path will be connected to the initial point of another.

Concatenate another path in such a way that the last point of this path coincides the first point of another by translating another.

Return the reversed path, which contains elements of points in the reverse order.

Translate this path using a linear transformation f.

Compute the point in the path at which the total distance covered equals distance.

Translate this path so that the initial data point is at the specified vector.

Translate this path so that the initial data point is at zero.

Compute a vector parallel to a tangent of the path passing pointAt(distance).

This function returns a None when the path is empty. Otherwise, if we let p denote pointAt(distance), this function returns a vector by the following rules:

if distance is zero and p equals the starting point of the path, the returned vector is parallel to the line segment outgoing from p
if distance equals totalDistance and p equals the last point of the path, the returned vector is parallel to the line segment incoming into p
if p is at some sampling point of the curve, let v1 and v2 be unit vectors parallel to the line segments incoming into (resp. outgoing from) p, and:
- if v1 is the opposite of v2 (equals v2.negate) then the returned vector is parallel to v1
- otherwise the returned vector is parallel to v1 + v2.

Translate the entire path with vector2D.

Concrete fields

The partial sum of arc length of this discrete path. n th element of this Vector contains a total distance travelled from the first point upto n th element in points.

This sequence is increasing, because the field is ordered and norm returns non-negative field elements.

Total length of this path.