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factory_nurbs.go
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factory_nurbs.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/utl"
)
// facNurbsT defines a structure to implement a factory of NURBS
type facNurbsT struct{}
// FactoryNurbs generates NURBS'
var FactoryNurbs = facNurbsT{}
// 2D curves //////////////////////////////////////////////////////////////////////////////////////
// Curve2dExample1 generates a 1D NURBS curve (example 1)
func (o facNurbsT) Curve2dExample1() (curve *Nurbs) {
verts := [][]float64{
{0.0, 0.0, 0, 1},
{1.0, 0.2, 0, 1},
{0.5, 1.5, 0, 1},
{2.5, 2.0, 0, 1},
{2.0, 0.4, 0, 1},
{3.0, 0.0, 0, 1},
}
knots := [][]float64{
{0, 0, 0, 0, 0.3, 0.7, 1, 1, 1, 1},
}
curve = NewNurbs(1, []int{3}, knots)
curve.SetControl(verts, utl.IntRange(len(verts)))
return
}
// Curve2dExample2 generates a 1D NURBS curve (example 2)
func (o facNurbsT) Curve2dExample2() (curve *Nurbs) {
verts := [][]float64{
{0.00, 0.00, 0, 0.80}, // 0
{0.25, 0.15, 0, 1.00}, // 1
{0.50, 0.00, 0, 0.70}, // 2
{0.75, 0.00, 0, 1.20}, // 3
{1.00, 0.10, 0, 1.10}, // 4
}
knots := [][]float64{
{0, 0, 0, 1, 2, 3, 3, 3},
}
curve = NewNurbs(1, []int{2}, knots)
curve.SetControl(verts, utl.IntRange(len(verts)))
return
}
// Curve2dCircle generates a 1D NURBS representing the circle curve
func (o facNurbsT) Curve2dCircle(xc, yc, r float64) (curve *Nurbs) {
xa, xb := xc-r, xc+r
ya, yb := yc-r, yc+r
verts := [][]float64{
{xb, yc, 0, 1.0},
{xb, yb, 0, 1.0 / math.Sqrt2},
{xc, yb, 0, 1.0},
{xa, yb, 0, 1.0 / math.Sqrt2},
{xa, yc, 0, 1.0},
{xa, ya, 0, 1.0 / math.Sqrt2},
{xc, ya, 0, 1.0},
{xb, ya, 0, 1.0 / math.Sqrt2},
{xb, yc, 0, 1.0},
}
knots := [][]float64{
{0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4}, // only along first dimension
}
curve = NewNurbs(1, []int{2}, knots)
curve.SetControl(verts, utl.IntRange(len(verts)))
return
}
// Curve2dQuarterCircle generates a 1D NURBS representing a quarter of circle
func (o facNurbsT) Curve2dQuarterCircle(xc, yc, r float64) (curve *Nurbs) {
verts := [][]float64{
{xc + r, yc, 0, math.Sqrt2},
{xc + r, yc + r, 0, 1.0},
{xc, yc + r, 0, math.Sqrt2},
}
knots := [][]float64{
{0, 0, 0, 1, 1, 1}, // only along first dimension
}
curve = NewNurbs(1, []int{2}, knots)
curve.SetControl(verts, utl.IntRange(len(verts)))
return
}
// 2D surfaces ////////////////////////////////////////////////////////////////////////////////////
// Surf2dRectangleQL generates a 2D NURBS surface with x being quadratic and y being linear
func (o facNurbsT) Surf2dRectangleQL(x0, y0, dx, dy float64) (surf *Nurbs) {
xm, xf, yf := x0+dx/2.0, x0+dx, y0+dy
verts := [][]float64{
{x0, y0, 0.0, 1.0},
{xm, y0, 0.0, 1.0},
{xf, y0, 0.0, 1.0},
{x0, yf, 0.0, 1.0},
{xm, yf, 0.0, 1.0},
{xf, yf, 0.0, 1.0},
}
knots := [][]float64{
{0, 0, 0, 1, 1, 1},
{0, 0, 1, 1},
}
surf = NewNurbs(2, []int{2, 1}, knots)
surf.SetControl(verts, utl.IntRange(len(verts)))
return
}
// Surf2dQuarterRing generates a 2D NURBS representing a quarter of ring
// a, b -- inner and outer radii
func (o facNurbsT) Surf2dQuarterRing(xc, yc, a, b float64) (surf *Nurbs) {
verts := [][]float64{
{xc + a, yc, 0, math.Sqrt2},
{xc + b, yc, 0, math.Sqrt2},
{xc + a, yc + a, 0, 1.0},
{xc + b, yc + b, 0, 1.0},
{xc, yc + a, 0, math.Sqrt2},
{xc, yc + b, 0, math.Sqrt2},
}
knots := [][]float64{
{0, 0, 1, 1},
{0, 0, 0, 1, 1, 1},
}
surf = NewNurbs(2, []int{1, 2}, knots)
surf.SetControl(verts, utl.IntRange(len(verts)))
return
}
// Surf2dExample1 generates a 2D NURBS of a 2D strip (x-quadratic, y-linear) (example 1)
func (o facNurbsT) Surf2dExample1() (surf *Nurbs) {
verts := [][]float64{
{0.00, 0.00, 0, 0.80}, // 0
{0.25, 0.15, 0, 1.00}, // 1
{0.50, 0.00, 0, 0.70}, // 2
{0.75, 0.00, 0, 1.20}, // 3
{1.00, 0.10, 0, 1.10}, // 4
{0.00, 0.40, 0, 0.90}, // 5
{0.25, 0.55, 0, 0.60}, // 6
{0.50, 0.40, 0, 1.50}, // 7
{0.75, 0.40, 0, 1.40}, // 8
{1.00, 0.50, 0, 0.50}, // 9
}
knots := [][]float64{
{0, 0, 0, 1, 2, 3, 3, 3},
{0, 0, 1, 1},
}
surf = NewNurbs(2, []int{2, 1}, knots)
surf.SetControl(verts, utl.IntRange(len(verts)))
return
}
// Surf2dQuarterPlateHole1 generates a 2D NURBS of a quarter of plate with hole (quadratic)
func (o facNurbsT) Surf2dQuarterPlateHole1() (surf *Nurbs) {
verts := [][]float64{
{-1.000000000000000e+00, 0.000000000000000e+00, 0, 1.000000000000000e+00},
{-1.000000000000000e+00, 4.142135623730951e-01, 0, 8.535533905932737e-01},
{-4.142135623730951e-01, 1.000000000000000e+00, 0, 8.535533905932737e-01},
{0.000000000000000e+00, 1.000000000000000e+00, 0, 1.000000000000000e+00},
{-2.500000000000000e+00, 0.000000000000000e+00, 0, 1.000000000000000e+00},
{-2.500000000000000e+00, 7.500000000000000e-01, 0, 1.000000000000000e+00},
{-7.500000000000000e-01, 2.500000000000000e+00, 0, 1.000000000000000e+00},
{0.000000000000000e+00, 2.500000000000000e+00, 0, 1.000000000000000e+00},
{-4.000000000000000e+00, 0.000000000000000e+00, 0, 1.000000000000000e+00},
{-4.000000000000000e+00, 4.000000000000000e+00, 0, 1.000000000000000e+00},
{0.000000000000000e+00, 4.000000000000000e+00, 0, 1.000000000000000e+00},
}
knots := [][]float64{
{0, 0, 0, 0.5, 1, 1, 1},
{0, 0, 0, 1, 1, 1},
}
surf = NewNurbs(2, []int{2, 2}, knots)
// repeated
// V V
surf.SetControl(verts, []int{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 10})
return
}
// 3D surfaces ////////////////////////////////////////////////////////////////////////////////////
// Surf3dCylinder generates a 3D NURBS representing the surface of a cyliner
func (o facNurbsT) Surf3dCylinder(xc, yc, zc, r, h float64) (curve *Nurbs) {
xa, xb := xc-r, xc+r
ya, yb := yc-r, yc+r
verts := [][]float64{
{xb, yc, zc, 1.0},
{xb, yb, zc, 1.0 / math.Sqrt2},
{xc, yb, zc, 1.0},
{xa, yb, zc, 1.0 / math.Sqrt2},
{xa, yc, zc, 1.0},
{xa, ya, zc, 1.0 / math.Sqrt2},
{xc, ya, zc, 1.0},
{xb, ya, zc, 1.0 / math.Sqrt2},
{xb, yc, zc, 1.0},
{xb, yc, zc + h, 1.0},
{xb, yb, zc + h, 1.0 / math.Sqrt2},
{xc, yb, zc + h, 1.0},
{xa, yb, zc + h, 1.0 / math.Sqrt2},
{xa, yc, zc + h, 1.0},
{xa, ya, zc + h, 1.0 / math.Sqrt2},
{xc, ya, zc + h, 1.0},
{xb, ya, zc + h, 1.0 / math.Sqrt2},
{xb, yc, zc + h, 1.0},
}
knots := [][]float64{
{0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4},
{0, 0, 1, 1},
}
curve = NewNurbs(2, []int{2, 1}, knots)
curve.SetControl(verts, utl.IntRange(len(verts)))
return
}
// Surf3dTorus generates a NURBS toroidal surface
// r -- is the tube radius
// R -- is the distance from the centre of the torus to the centre of the tube
func (o facNurbsT) Surf3dTorus(xc, yc, zc, r, R float64) (surf *Nurbs) {
a, b := R-r, R+r
s, h := 1.0/math.Sqrt2, 0.5
verts := [][]float64{
// 1
{xc + R, yc, zc - r, 1},
{xc + b, yc, zc - r, s},
{xc + b, yc, zc + 0, 1},
{xc + b, yc, zc + r, s},
{xc + R, yc, zc + r, 1},
{xc + a, yc, zc + r, s},
{xc + a, yc, zc + 0, 1},
{xc + a, yc, zc - r, s},
{xc + R, yc, zc - r, 1},
// 2
{xc + R, yc + R, zc - r, s},
{xc + b, yc + b, zc - r, h},
{xc + b, yc + b, zc + 0, s},
{xc + b, yc + b, zc + r, h},
{xc + R, yc + R, zc + r, s},
{xc + a, yc + a, zc + r, h},
{xc + a, yc + a, zc + 0, s},
{xc + a, yc + a, zc - r, h},
{xc + R, yc + R, zc - r, s},
// 3
{xc, yc + R, zc - r, 1},
{xc, yc + b, zc - r, s},
{xc, yc + b, zc + 0, 1},
{xc, yc + b, zc + r, s},
{xc, yc + R, zc + r, 1},
{xc, yc + a, zc + r, s},
{xc, yc + a, zc + 0, 1},
{xc, yc + a, zc - r, s},
{xc, yc + R, zc - r, 1},
// 4
{xc - R, yc + R, zc - r, s},
{xc - b, yc + b, zc - r, h},
{xc - b, yc + b, zc + 0, s},
{xc - b, yc + b, zc + r, h},
{xc - R, yc + R, zc + r, s},
{xc - a, yc + a, zc + r, h},
{xc - a, yc + a, zc + 0, s},
{xc - a, yc + a, zc - r, h},
{xc - R, yc + R, zc - r, s},
// 5
{xc - R, yc, zc - r, 1},
{xc - b, yc, zc - r, s},
{xc - b, yc, zc + 0, 1},
{xc - b, yc, zc + r, s},
{xc - R, yc, zc + r, 1},
{xc - a, yc, zc + r, s},
{xc - a, yc, zc + 0, 1},
{xc - a, yc, zc - r, s},
{xc - R, yc, zc - r, 1},
// 6
{xc - R, yc - R, zc - r, s},
{xc - b, yc - b, zc - r, h},
{xc - b, yc - b, zc + 0, s},
{xc - b, yc - b, zc + r, h},
{xc - R, yc - R, zc + r, s},
{xc - a, yc - a, zc + r, h},
{xc - a, yc - a, zc + 0, s},
{xc - a, yc - a, zc - r, h},
{xc - R, yc - R, zc - r, s},
// 7
{xc, yc - R, zc - r, 1},
{xc, yc - b, zc - r, s},
{xc, yc - b, zc + 0, 1},
{xc, yc - b, zc + r, s},
{xc, yc - R, zc + r, 1},
{xc, yc - a, zc + r, s},
{xc, yc - a, zc + 0, 1},
{xc, yc - a, zc - r, s},
{xc, yc - R, zc - r, 1},
// 8
{xc + R, yc + -R, zc - r, s},
{xc + b, yc + -b, zc - r, h},
{xc + b, yc + -b, zc + 0, s},
{xc + b, yc + -b, zc + r, h},
{xc + R, yc + -R, zc + r, s},
{xc + a, yc + -a, zc + r, h},
{xc + a, yc + -a, zc + 0, s},
{xc + a, yc + -a, zc - r, h},
{xc + R, yc + -R, zc - r, s},
// 9
{xc + R, yc, zc - r, 1},
{xc + b, yc, zc - r, s},
{xc + b, yc, zc + 0, 1},
{xc + b, yc, zc + r, s},
{xc + R, yc, zc + r, 1},
{xc + a, yc, zc + r, s},
{xc + a, yc, zc + 0, 1},
{xc + a, yc, zc - r, s},
{xc + R, yc, zc - r, 1},
}
knots := [][]float64{
{0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4},
{0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4},
}
surf = NewNurbs(2, []int{2, 2}, knots)
surf.SetControl(verts, utl.IntRange(len(verts)))
return
}
// Surf3dQuarterHemisphere generates a NURBS toroidal surface
func (o facNurbsT) Surf3dQuarterHemisphere(xc, yc, zc, r float64) (surf *Nurbs) {
s := math.Sqrt2 / 2.0
verts := [][]float64{
{xc + r, yc + 0, zc + 0, 1},
{xc + r, yc + r, zc + 0, s},
{xc + 0, yc + r, zc + 0, 1},
{xc + r, yc + 0, zc + r, s},
{xc + r, yc + r, zc + r, 0.5},
{xc + 0, yc + r, zc + r, s},
{xc + 0, yc + 0, zc + r, 1},
{xc + 0, yc + 0, zc + r, s},
{xc + 0, yc + 0, zc + r, 1},
}
knots := [][]float64{
{0, 0, 0, 1, 1, 1},
{0, 0, 0, 1, 1, 1},
}
surf = NewNurbs(2, []int{2, 2}, knots)
surf.SetControl(verts, utl.IntRange(len(verts)))
return
}
// Solids /////////////////////////////////////////////////////////////////////////////////////////
// SolidHex generates a solid hexahedron
func (o facNurbsT) SolidHex(corners [][]float64) (solid *Nurbs) {
verts := utl.Alloc(8, 4)
for i := 0; i < 8; i++ {
for j := 0; j < 3; j++ {
verts[i][j] = corners[i][j]
}
verts[i][3] = 1.0
}
knots := [][]float64{
{0, 0, 1, 1},
{0, 0, 1, 1},
{0, 0, 1, 1},
}
solid = NewNurbs(3, []int{1, 1, 1}, knots)
solid.SetControl(verts, utl.IntRange(len(verts)))
return
}
// SolidQuarterRing generates a solid NURBS representing a quarter of ring
// xc,yc,yc -- centre
// a,b -- inner and outer radii [b > a]
// h -- thickness along x-direction
func (o facNurbsT) SolidQuarterRing(xc, yc, zc, a, b, h float64) (solid *Nurbs) {
verts := [][]float64{
{xc + 0, yc + a, zc + 0, math.Sqrt2},
{xc + h, yc + a, zc + 0, math.Sqrt2},
{xc + 0, yc + b, zc + 0, math.Sqrt2},
{xc + h, yc + b, zc + 0, math.Sqrt2},
{xc + 0, yc + a, zc + a, 1.0},
{xc + h, yc + a, zc + a, 1.0},
{xc + 0, yc + b, zc + b, 1.0},
{xc + h, yc + b, zc + b, 1.0},
{xc + 0, yc + 0, zc + a, math.Sqrt2},
{xc + h, yc + 0, zc + a, math.Sqrt2},
{xc + 0, yc + 0, zc + b, math.Sqrt2},
{xc + h, yc + 0, zc + b, math.Sqrt2},
}
knots := [][]float64{
{0, 0, 1, 1},
{0, 0, 1, 1},
{0, 0, 0, 1, 1, 1},
}
solid = NewNurbs(3, []int{1, 1, 2}, knots)
solid.SetControl(verts, utl.IntRange(len(verts)))
return
}