WIP: splines
This commit is contained in:
Josh Deprez
parent
6ebd3e0329
commit
c74d915542
6 changed files with 329 additions and 83 deletions
63
geom/float2.go
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63
geom/float2.go
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@ -0,0 +1,63 @@
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package geom
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import "fmt"
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// Float2 is an element of float64^2
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type Float2 struct {
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X, Y float64
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}
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// String returns a string representation of p like "(3.0,4.0,5.0)".
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func (p Float2) String() string {
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return fmt.Sprintf("(%f,%f)", p.X, p.Y)
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}
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// Add performs vector addition.
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func (p Float2) Add(q Float2) Float2 {
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return Float2{p.X + q.X, p.Y + q.Y}
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}
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// Sub performs vector subtraction.
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func (p Float2) Sub(q Float2) Float2 {
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return p.Add(q.Neg())
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}
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// CMul performs componentwise multiplication.
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func (p Float2) CMul(q Float2) Float2 {
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return Float2{p.X * q.X, p.Y * q.Y}
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}
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// Mul performs scalar multiplication.
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func (p Float2) Mul(k float64) Float2 {
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return Float2{p.X * k, p.Y * k}
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}
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// CDiv performs componentwise division.
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func (p Float2) CDiv(q Float2) Float2 {
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return Float2{p.X / q.X, p.Y / q.Y}
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}
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// Div performs scalar division by k.
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func (p Float2) Div(k float64) Float2 {
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return Float2{p.X / k, p.Y / k}
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}
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// Neg returns the vector pointing in the opposite direction.
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func (p Float2) Neg() Float2 {
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return Float2{-p.X, -p.Y}
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}
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// Coord returns the components of the vector.
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func (p Float2) Coord() (x, y float64) {
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return p.X, p.Y
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}
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// Sign returns a sign vector.
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func (p Float2) Sign() Float2 {
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return Float2{FSign(p.X), FSign(p.Y)}
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}
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// Dot returns the dot product of the two vectors.
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func (p Float2) Dot(q Float2) float64 {
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return p.X*q.X + p.Y*q.Y
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}
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63
geom/float3.go
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63
geom/float3.go
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@ -0,0 +1,63 @@
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package geom
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import "fmt"
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// Float3 is an element of float64^3.
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type Float3 struct {
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X, Y, Z float64
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}
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// String returns a string representation of p like "(3.0,4.0,5.0)".
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func (p Float3) String() string {
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return fmt.Sprintf("(%f,%f,%f)", p.X, p.Y, p.Z)
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}
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// Add performs vector addition.
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func (p Float3) Add(q Float3) Float3 {
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return Float3{p.X + q.X, p.Y + q.Y, p.Z + q.Z}
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}
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// Sub performs vector subtraction.
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func (p Float3) Sub(q Float3) Float3 {
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return p.Add(q.Neg())
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}
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// CMul performs componentwise multiplication.
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func (p Float3) CMul(q Float3) Float3 {
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return Float3{p.X * q.X, p.Y * q.Y, p.Z * q.Z}
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}
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// Mul performs scalar multiplication.
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func (p Float3) Mul(k float64) Float3 {
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return Float3{p.X * k, p.Y * k, p.Z * k}
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}
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// CDiv performs componentwise division.
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func (p Float3) CDiv(q Float3) Float3 {
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return Float3{p.X / q.X, p.Y / q.Y, p.Z / q.Z}
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}
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// Div performs scalar division by k.
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func (p Float3) Div(k float64) Float3 {
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return Float3{p.X / k, p.Y / k, p.Z / k}
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}
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// Neg returns the vector pointing in the opposite direction.
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func (p Float3) Neg() Float3 {
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return Float3{-p.X, -p.Y, -p.Z}
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}
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// Coord returns the components of the vector.
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func (p Float3) Coord() (x, y, z float64) {
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return p.X, p.Y, p.Z
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}
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// Sign returns a sign vector.
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func (p Float3) Sign() Float3 {
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return Float3{FSign(p.X), FSign(p.Y), FSign(p.Z)}
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}
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// Dot returns the dot product of the two vectors.
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func (p Float3) Dot(q Float3) float64 {
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return p.X*q.X + p.Y*q.Y + p.Z*q.Z
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}
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@ -17,7 +17,6 @@ limitations under the License.
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package geom
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import (
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"fmt"
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"image"
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"strconv"
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)
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@ -96,85 +95,3 @@ func (p Int3) Sign() Int3 {
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func (p Int3) Dot(q Int3) int {
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return p.X*q.X + p.Y*q.Y + p.Z*q.Z
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}
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// Sign returns the sign of the int (-1, 0, or 1).
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func Sign(m int) int {
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if m == 0 {
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return 0
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}
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if m < 0 {
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return -1
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}
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return 1
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}
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// FSign returns the sign of the float64 (-1, 0, or 1).
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func FSign(m float64) float64 {
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if m == 0 {
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return 0
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}
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if m < 0 {
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return -1
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}
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return 1
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}
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// Float3 is an element of float64^3.
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type Float3 struct {
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X, Y, Z float64
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}
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// String returns a string representation of p like "(3.0,4.0,5.0)".
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func (p Float3) String() string {
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return fmt.Sprintf("(%f,%f,%f)", p.X, p.Y, p.Z)
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}
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// Add performs vector addition.
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func (p Float3) Add(q Float3) Float3 {
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return Float3{p.X + q.X, p.Y + q.Y, p.Z + q.Z}
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}
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// Sub performs vector subtraction.
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func (p Float3) Sub(q Float3) Float3 {
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return p.Add(q.Neg())
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}
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// CMul performs componentwise multiplication.
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func (p Float3) CMul(q Float3) Float3 {
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return Float3{p.X * q.X, p.Y * q.Y, p.Z * q.Z}
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}
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// Mul performs scalar multiplication.
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func (p Float3) Mul(k float64) Float3 {
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return Float3{p.X * k, p.Y * k, p.Z * k}
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}
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// CDiv performs componentwise division.
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func (p Float3) CDiv(q Float3) Float3 {
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return Float3{p.X / q.X, p.Y / q.Y, p.Z / q.Z}
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}
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// Div performs scalar division by k.
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func (p Float3) Div(k float64) Float3 {
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return Float3{p.X / k, p.Y / k, p.Z / k}
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}
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// Neg returns the vector pointing in the opposite direction.
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func (p Float3) Neg() Float3 {
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return Float3{-p.X, -p.Y, -p.Z}
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}
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// Coord returns the components of the vector.
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func (p Float3) Coord() (x, y, z float64) {
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return p.X, p.Y, p.Z
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}
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// Sign returns a sign vector.
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func (p Float3) Sign() Float3 {
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return Float3{FSign(p.X), FSign(p.Y), FSign(p.Z)}
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}
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// Dot returns the dot product of the two vectors.
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func (p Float3) Dot(q Float3) float64 {
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return p.X*q.X + p.Y*q.Y + p.Z*q.Z
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}
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24
geom/misc.go
24
geom/misc.go
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@ -39,3 +39,27 @@ func CFloat(p image.Point) (x, y float64) {
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func Dot(p, q image.Point) int {
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return p.X*q.X + p.Y*q.Y
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}
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// ---------- Some other helpers ----------
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// FSign returns the sign of the float64 (-1, 0, or 1).
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func FSign(m float64) float64 {
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if m == 0 {
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return 0
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}
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if m < 0 {
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return -1
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}
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return 1
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}
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// Sign returns the sign of the int (-1, 0, or 1).
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func Sign(m int) int {
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if m == 0 {
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return 0
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}
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if m < 0 {
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return -1
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}
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return 1
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}
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100
geom/spline.go
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100
geom/spline.go
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package geom
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import (
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"errors"
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"fmt"
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"sort"
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)
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// LinearSpline implements a linear spline.
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type LinearSpline struct {
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Points []Float2
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deriv []float64 // slope of segment between points i and i+1
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}
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// Prepare sorts the points and computes internal information.
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func (s *LinearSpline) Prepare() error {
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if len(s.Points) < 1 {
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return errors.New("spline needs at least 1 point")
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}
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// Ensure Points is sorted.
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sort.Slice(s.Points, func(i, j int) bool {
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return s.Points[i].X < s.Points[j].X
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})
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// Check for points with equal X and compute derivatives
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s.deriv = make([]float64, len(s.Points)-1)
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for i := range s.Points[1:] {
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if s.Points[i].X == s.Points[i+1].X {
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return fmt.Errorf("spline value defined twice [%v, %v]", s.Points[i], s.Points[i+1])
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}
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s.deriv[i] = (s.Points[i+1].Y - s.Points[i].Y) / (s.Points[i+1].X - s.Points[i].X)
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}
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return nil
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}
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// Interpolate, given x, returns y where (x,y) is a point on the spline.
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// If x is outside the spline, it extrapolates from either the first or
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// last segments of the spline.
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func (s *LinearSpline) Interpolate(x float64) float64 {
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N := len(s.Points)
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if N == 1 {
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return s.Points[0].Y
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}
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if x < s.Points[1].X {
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// Comes before the end of the first segment
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return s.Points[0].Y + (x-s.Points[0].X)*s.deriv[0]
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}
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if x > s.Points[N-2].X {
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// Comes after the start of the last segment
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return s.Points[N-1].Y + (x-s.Points[N-1].X)*s.deriv[N-2]
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}
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// Somewhere in the middle
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i := sort.Search(N, func(n int) bool {
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return x <= s.Points[n].X
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})
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if x == s.Points[i].X {
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// Hit a point exactly
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return s.Points[i].Y
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}
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// In the interval between point i and point i+1
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return s.Points[i].Y + (x-s.Points[i].X)*s.deriv[i]
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}
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// CubicSpline implements a cubic spline.
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type CubicSpline struct {
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// Points on the spline
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Points []Float2
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deriv, deriv2 []float64
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}
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// Prepare
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func (s *CubicSpline) Prepare() error {
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if len(s.Points) < 1 {
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return errors.New("spline needs at least 1 point")
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}
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// Ensure Points is sorted.
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sort.Slice(s.Points, func(i, j int) bool {
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return s.Points[i].X < s.Points[j].X
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})
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// Check for points with equal X.
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for i := range s.Points[1:] {
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if s.Points[i].X == s.Points[i+1].X {
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return fmt.Errorf("spline value defined twice [%v, %v]", s.Points[i], s.Points[i+1])
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}
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}
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// TODO: compute deriv and deriv2
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return nil
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}
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func (s *CubicSpline) Interpolate(x float64) float64 {
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N := len(s.Points)
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if N == 1 {
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return s.Points[0].Y
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}
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// TODO
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return 0
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}
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79
geom/spline_test.go
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79
geom/spline_test.go
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package geom
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import "testing"
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func TestLinearSplineNoPoints(t *testing.T) {
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s := &LinearSpline{}
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if err := s.Prepare(); err == nil {
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t.Errorf("s.Prepare() = %v, want error", err)
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}
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}
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func TestLinearSplineEqualXPoints(t *testing.T) {
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s := &LinearSpline{
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Points: []Float2{{-5, 1}, {-2, 7}, {-2, -3}, {0, 2}, {3, -2}},
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}
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if err := s.Prepare(); err == nil {
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t.Errorf("s.Prepare() = %v, want error", err)
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}
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}
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func TestLinearSplineOnePoint(t *testing.T) {
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s := &LinearSpline{
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Points: []Float2{{-2, -3}},
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}
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if err := s.Prepare(); err != nil {
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t.Errorf("s.Prepare() = %v, want nil", err)
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}
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for _, x := range []float64{-5, -4, -2, 0, 1, 7} {
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if got, want := s.Interpolate(x), float64(-3); got != want {
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t.Errorf("s.Interpolate(%v) = %v, want %v", x, got, want)
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}
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}
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}
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func TestLinearSpline(t *testing.T) {
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s := &LinearSpline{
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Points: []Float2{{-7, -2}, {-5, 1}, {-3, 0}, {-2, -3}, {0, 2}, {1, -5}, {3, -2}, {4, 4}},
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}
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if err := s.Prepare(); err != nil {
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t.Errorf("s.Prepare() = %v, want nil", err)
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}
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tests := []struct {
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x, want float64
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}{
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{x: -8, want: -3.5},
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{x: -7.5, want: -2.75},
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{x: -7, want: -2},
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{x: -6.5, want: -1.25},
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{x: -6, want: -0.5},
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{x: -5.5, want: 0.25},
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{x: -5, want: 1},
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{x: -4.5, want: 4.5},
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{x: -4, want: 3},
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{x: -3.5, want: 1.5},
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{x: -3, want: 0},
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{x: -2.5, want: -4.25},
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{x: -2, want: -3},
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{x: -1.5, want: 12.5},
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{x: -1, want: 9},
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{x: -0.5, want: 5.5},
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{x: 0, want: 2},
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{x: 0.5, want: -5.75},
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{x: 1, want: -5},
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{x: 1.5, want: -11},
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{x: 2, want: -8},
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{x: 2.5, want: -5},
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{x: 3, want: -2},
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{x: 3.5, want: 1},
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{x: 4, want: 4},
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{x: 4.5, want: 7},
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{x: 5, want: 10},
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{x: 5.5, want: 13},
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}
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for _, test := range tests {
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if got := s.Interpolate(test.x); got != test.want {
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t.Errorf("s.Interpolate(%v) = %v, want %v", test.x, got, test.want)
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}
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}
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}
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