bezier

Documentation

Index

• Variables
• type Bezier
  • func NewBezier(use3d bool, points ...Point) (*Bezier, error)
  • func (b *Bezier) Curvature(t float64) CurvatureVector
  • func (b *Bezier) Get(t float64) Point
  • func (b *Bezier) Length() float64
  • func (b *Bezier) Normal(t float64) Point
• type CurvatureVector
• type DerivativeFunc
• type Point
  • func CreateHobbySpline(points []Point, omega float64) ([]Point, error)
  • func NaturalCubicSpline(points []Point) ([]Point, error)
  • func Normalize(v Point) Point
  • func Rotate(v Point, angle float64) Point
  • func Scale(v Point, s float64) Point
  • func (v *Point) Angle() float64
  • func (v Point) Length() float64

Variables

var Cvalues = []float64{
	0.1279381953467521569740561652246953718517,
	0.1279381953467521569740561652246953718517,
	0.1258374563468282961213753825111836887264,
	0.1258374563468282961213753825111836887264,
	0.121670472927803391204463153476262425607,
	0.121670472927803391204463153476262425607,
	0.1155056680537256013533444839067835598622,
	0.1155056680537256013533444839067835598622,
	0.1074442701159656347825773424466062227946,
	0.1074442701159656347825773424466062227946,
	0.0976186521041138882698806644642471544279,
	0.0976186521041138882698806644642471544279,
	0.086190161531953275917185202983742667185,
	0.086190161531953275917185202983742667185,
	0.0733464814110803057340336152531165181193,
	0.0733464814110803057340336152531165181193,
	0.0592985849154367807463677585001085845412,
	0.0592985849154367807463677585001085845412,
	0.0442774388174198061686027482113382288593,
	0.0442774388174198061686027482113382288593,
	0.0285313886289336631813078159518782864491,
	0.0285313886289336631813078159518782864491,
	0.0123412297999871995468056670700372915759,
	0.0123412297999871995468056670700372915759,
}

Legendre-Gauss weights with n=24 (w_i values, defined by a function linked to in the Bezier primer article)

var Tvalues = []float64{
	-0.0640568928626056260850430826247450385909,
	0.0640568928626056260850430826247450385909,
	-0.1911188674736163091586398207570696318404,
	0.1911188674736163091586398207570696318404,
	-0.3150426796961633743867932913198102407864,
	0.3150426796961633743867932913198102407864,
	-0.4337935076260451384870842319133497124524,
	0.4337935076260451384870842319133497124524,
	-0.5454214713888395356583756172183723700107,
	0.5454214713888395356583756172183723700107,
	-0.6480936519369755692524957869107476266696,
	0.6480936519369755692524957869107476266696,
	-0.7401241915785543642438281030999784255232,
	0.7401241915785543642438281030999784255232,
	-0.8200019859739029219539498726697452080761,
	0.8200019859739029219539498726697452080761,
	-0.8864155270044010342131543419821967550873,
	0.8864155270044010342131543419821967550873,
	-0.9382745520027327585236490017087214496548,
	0.9382745520027327585236490017087214496548,
	-0.9747285559713094981983919930081690617411,
	0.9747285559713094981983919930081690617411,
	-0.9951872199970213601799974097007368118745,
	0.9951872199970213601799974097007368118745,
}

Legendre-Gauss abscissae with n=24 (x_i values, defined at i=n as the roots of the nth order Legendre polynomial Pn(x))

Types

type Bezier

type Bezier struct {
	Points []Point
	// contains filtered or unexported fields
}

func NewBezier

func NewBezier(use3d bool, points ...Point) (*Bezier, error)

NewBezier creates a new Bezier curve with the given points.

func (*Bezier) Curvature

func (b *Bezier) Curvature(t float64) CurvatureVector

func (*Bezier) Get

func (b *Bezier) Get(t float64) Point

func (*Bezier) Length

func (b *Bezier) Length() float64

func (*Bezier) Normal

func (b *Bezier) Normal(t float64) Point

type CurvatureVector

type CurvatureVector struct {
	K float64
	R float64
	// contains filtered or unexported fields
}

type DerivativeFunc

type DerivativeFunc func(float64) Point

type Point

type Point struct {
	X float64
	Y float64
	Z float64
	// contains filtered or unexported fields
}

func CreateHobbySpline

func CreateHobbySpline(points []Point, omega float64) ([]Point, error)

CreateHobbySpline: given a set of points, fit a Bézier spline to them. The chosen splines tend to have pleasing, rounded shapes.

The output array will have 3n - 2 points where n is the number of input points. The output will contain every point in the input (these become knots in the Bézier spline), interspersed with pairs of new points which define positions of handle points on the spline. All points are in the same coordinate space.

func NaturalCubicSpline

func NaturalCubicSpline(points []Point) ([]Point, error)

NaturalCubicSpline creates cubic Bezier curves that naturally interpolate through the given points.

func Normalize

func Normalize(v Point) Point

func Rotate

func Rotate(v Point, angle float64) Point

func Scale

func Scale(v Point, s float64) Point

func (*Point) Angle

func (v *Point) Angle() float64

func (Point) Length

func (v Point) Length() float64