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basicgeom.go
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basicgeom.go
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// Copyright 2016 The Gosl Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package gm
import (
"math"
"github.com/cpmech/gosl/io"
)
// Point holds the Cartesian coordinates of a point in 3D space
type Point struct {
X, Y, Z float64
}
// Segment represents a directed segment from A to B
type Segment struct {
A, B *Point
}
// Point methods /////////////////////////////////////////////////////////////////////////////////////
// NewCopy creates a new copy of Point
func (o *Point) NewCopy() *Point {
return &Point{o.X, o.Y, o.Z}
}
// NewDisp creates a new copy of Point displaced by dx, dy, dz
func (o *Point) NewDisp(dx, dy, dz float64) *Point {
return &Point{o.X + dx, o.Y + dy, o.Z + dz}
}
// String outputs Point
func (o *Point) String() string {
return io.Sf("{%g, %g, %g}", o.X, o.Y, o.Z)
}
// DistPointPoint computes the unsigned distance from a to b
func DistPointPoint(a, b *Point) float64 {
return math.Sqrt((a.X-b.X)*(a.X-b.X) +
(a.Y-b.Y)*(a.Y-b.Y) +
(a.Z-b.Z)*(a.Z-b.Z))
}
// Segment methods ///////////////////////////////////////////////////////////////////////////////////
// Len computes the length of Segment == Euclidean norm
func (o *Segment) Len() float64 {
return DistPointPoint(o.A, o.B)
}
// New creates a new Segment scaled by m and starting from A
func (o *Segment) New(m float64) *Segment {
return &Segment{o.A.NewCopy(), &Point{o.A.X + m*(o.B.X-o.A.X),
o.A.Y + m*(o.B.Y-o.A.Y),
o.A.Z + m*(o.B.Z-o.A.Z)}}
}
// Vector returns the vector representing Segment from A to B (scaled by m)
func (o *Segment) Vector(m float64) []float64 {
return []float64{m * (o.B.X - o.A.X),
m * (o.B.Y - o.A.Y),
m * (o.B.Z - o.A.Z)}
}
// String outputs Segment
func (o *Segment) String() string {
return io.Sf("{%v %v} len=%g", o.A, o.B, o.Len())
}
// NewSegment creates a new segment from a to b
func NewSegment(a, b *Point) *Segment {
return &Segment{a, b}
}
// Vector ////////////////////////////////////////////////////////////////////////////////////////////
// VecDot returns the dot product between two vectors
func VecDot(u, v []float64) float64 {
return u[0]*v[0] + u[1]*v[1] + u[2]*v[2]
}
// VecNorm returns the length (Euclidean norm) of a vector
func VecNorm(u []float64) float64 {
return math.Sqrt(u[0]*u[0] + u[1]*u[1] + u[2]*u[2])
}
// VecNew returns a new vector scaled by m
func VecNew(m float64, u []float64) []float64 {
return []float64{m * u[0], m * u[1], m * u[2]}
}
// VecNewAdd returns a new vector by adding two other vectors
// w := α*u + β*v
func VecNewAdd(α float64, u []float64, β float64, v []float64) []float64 {
return []float64{α*u[0] + β*v[0], α*u[1] + β*v[1], α*u[2] + β*v[2]}
}
// distance functions ////////////////////////////////////////////////////////////////////////////////
// DistPointLine computes the distance from p to line passing through a -> b
func DistPointLine(p, a, b *Point, tol float64, verbose bool) float64 {
ns := NewSegment(a, b)
vs := NewSegment(p, a)
nn := ns.Len()
if nn < tol { // point-point distance
if verbose {
io.Pfred("basicgeom.go: DistPointLine: __WARNING__ point-point distance too small:\n p=%v a=%v b=%v\n", p, a, b)
}
return vs.Len()
}
n := ns.Vector(1.0 / nn)
v := vs.Vector(1.0)
s := VecDot(v, n)
l := VecNewAdd(1, v, -s, n) // l := v - dot(v,n) * n
return VecNorm(l)
}
// locate functions //////////////////////////////////////////////////////////////////////////////////
// PointsLims returns the limits of a set of points
func PointsLims(pp []*Point) (cmin, cmax []float64) {
if len(pp) < 1 {
return []float64{0, 0, 0}, []float64{0, 0, 0}
}
cmin = []float64{pp[0].X, pp[0].Y, pp[0].Z}
cmax = []float64{pp[0].X, pp[0].Y, pp[0].Z}
for i := 1; i < len(pp); i++ {
if pp[i].X < cmin[0] {
cmin[0] = pp[i].X
}
if pp[i].Y < cmin[1] {
cmin[1] = pp[i].Y
}
if pp[i].Z < cmin[2] {
cmin[2] = pp[i].Z
}
if pp[i].X > cmax[0] {
cmax[0] = pp[i].X
}
if pp[i].Y > cmax[1] {
cmax[1] = pp[i].Y
}
if pp[i].Z > cmax[2] {
cmax[2] = pp[i].Z
}
}
return
}
// IsPointIn returns whether p is inside box with cMin and cMax
func IsPointIn(p *Point, cMin, cMax []float64, tol float64) bool {
if p.X < cMin[0]-tol || p.X > cMax[0]+tol {
return false
}
if p.Y < cMin[1]-tol || p.Y > cMax[1]+tol {
return false
}
if p.Z < cMin[2]-tol || p.Z > cMax[2]+tol {
return false
}
return true
}
// IsPointInLine returns whether p is inside line passing through a and b
func IsPointInLine(p, a, b *Point, zero, told, tolin float64) bool {
cmin, cmax := PointsLims([]*Point{a, b})
d := DistPointLine(p, a, b, zero, false)
if d < told && IsPointIn(p, cmin, cmax, tolin) {
return true
}
return false
}
/*
// WireLength returns the length of a wireframe
func WireLength(pp []*Point) (l float64) {
for xa, xb in zip(points[:-1], points[1:]) {
l += DistPointPoint(xa, xb)
}
return l
}
// DistAlongWire returns the distance of p along oriented line
// Input:
// points -- list of points defining wireframe
// Output:
// d -- total distance from p to first point in wireframe,
// negative value (-1.0) means point is outside line
func DistAlongWire(p, points, TolD=1e-10, TolIn=1e-10) {
p, l, k = array(p, dtype=float), 0.0, 0
for xa, xb in zip(points[:-1], points[1:]) {
if IsPointInLine(p, xa, xb, TolD, TolIn) {
return l + DistPointPoint(p, xa)
}
l += DistPointPoint(xa, xb)
}
return -1.0 // not found
}
*/