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feat: remove vtk dependency to calculate tetrahedron volume #417

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merged 3 commits into from
Jan 22, 2024
Merged

feat: remove vtk dependency to calculate tetrahedron volume #417

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a39fdbd
feat: remove vtk dependency to calculate tetrahedron volume
Jan 8, 2024
7e0c429
refactor: move determinant object to separate file under numerics
Jan 8, 2024
298db6c
fix: wrong import + removed vtk import
Jan 16, 2024
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20 changes: 15 additions & 5 deletions src/main/scala/scalismo/mesh/TetrahedralMesh.scala
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Original file line number Diff line number Diff line change
Expand Up @@ -16,11 +16,11 @@
package scalismo.mesh

import breeze.linalg.DenseVector
import scalismo.common._
import scalismo.geometry._
import scalismo.common.*
import scalismo.geometry.*
import scalismo.numerics.Determinant
import scalismo.transformations.Transformation
import scalismo.utils.Random
import vtk.vtkTetra

import scala.language.implicitConversions

Expand Down Expand Up @@ -160,8 +160,18 @@ case class TetrahedralMesh3D(pointSet: UnstructuredPoints[_3D], tetrahedralizati
val c = pointSet.point(tetrahedron.ptId3)
val d = pointSet.point(tetrahedron.ptId4)

// note: replace call to vtk with own implementation
val signedVolume = new vtkTetra().ComputeVolume(a.toArray, b.toArray, c.toArray, d.toArray)
val signedVolume = Determinant.det3x3(
b.x - a.x,
c.x - a.x,
d.x - a.x,
b.y - a.y,
c.y - a.y,
d.y - a.y,
b.z - a.z,
c.z - a.z,
d.z - a.z
) / 6

math.abs(signedVolume)
}

Expand Down
177 changes: 62 additions & 115 deletions src/main/scala/scalismo/mesh/boundingSpheres/BSIntersection.scala
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Original file line number Diff line number Diff line change
Expand Up @@ -17,6 +17,7 @@ package scalismo.mesh.boundingSpheres

import scalismo.geometry.{_3D, EuclideanVector, Point}
import scalismo.mesh.{BarycentricCoordinates, BarycentricCoordinates4}
import scalismo.numerics.Determinant

/**
* Helper function to calculate intersection points.
Expand All @@ -29,48 +30,48 @@ private[boundingSpheres] object BSIntersection {
b: EuclideanVector[_3D],
c: EuclideanVector[_3D]
): (Boolean, Point[_3D]) = {
val det = Determinantes.det3x3(a.x - b.x,
a.x - c.x,
val det = Determinant.det3x3(a.x - b.x,
a.x - c.x,
direction.x,
a.y - b.y,
a.y - c.y,
direction.y,
a.z - b.z,
a.z - c.z,
direction.z
)

val beta = Determinant.det3x3(a.x - point.x,
a.x - c.x,
direction.x,
a.y - point.y,
a.y - c.y,
direction.y,
a.z - point.z,
a.z - c.z,
direction.z
) / det

val gamma = Determinant.det3x3(a.x - b.x,
a.x - point.x,
direction.x,
a.y - b.y,
a.y - c.y,
a.y - point.y,
direction.y,
a.z - b.z,
a.z - c.z,
a.z - point.z,
direction.z
)

val beta = Determinantes.det3x3(a.x - point.x,
a.x - c.x,
direction.x,
a.y - point.y,
a.y - c.y,
direction.y,
a.z - point.z,
a.z - c.z,
direction.z
) / det

val gamma = Determinantes.det3x3(a.x - b.x,
a.x - point.x,
direction.x,
a.y - b.y,
a.y - point.y,
direction.y,
a.z - b.z,
a.z - point.z,
direction.z
) / det

val t = Determinantes.det3x3(a.x - b.x,
a.x - c.x,
a.x - point.x,
a.y - b.y,
a.y - c.y,
a.y - point.y,
a.z - b.z,
a.z - c.z,
a.z - point.z
val t = Determinant.det3x3(a.x - b.x,
a.x - c.x,
a.x - point.x,
a.y - b.y,
a.y - c.y,
a.y - point.y,
a.z - b.z,
a.z - c.z,
a.z - point.z
) / det

if (beta >= 0.0 && gamma >= 0.0 && beta + gamma <= 1.0) {
Expand All @@ -87,37 +88,37 @@ private[boundingSpheres] object BSIntersection {
b: EuclideanVector[_3D],
c: EuclideanVector[_3D]
): (Boolean, BarycentricCoordinates) = {
val det = Determinantes.det3x3(a.x - b.x,
a.x - c.x,
val det = Determinant.det3x3(a.x - b.x,
a.x - c.x,
direction.x,
a.y - b.y,
a.y - c.y,
direction.y,
a.z - b.z,
a.z - c.z,
direction.z
)

val beta = Determinant.det3x3(a.x - point.x,
a.x - c.x,
direction.x,
a.y - point.y,
a.y - c.y,
direction.y,
a.z - point.z,
a.z - c.z,
direction.z
) / det

val gamma = Determinant.det3x3(a.x - b.x,
a.x - point.x,
direction.x,
a.y - b.y,
a.y - c.y,
a.y - point.y,
direction.y,
a.z - b.z,
a.z - c.z,
a.z - point.z,
direction.z
)

val beta = Determinantes.det3x3(a.x - point.x,
a.x - c.x,
direction.x,
a.y - point.y,
a.y - c.y,
direction.y,
a.z - point.z,
a.z - c.z,
direction.z
) / det

val gamma = Determinantes.det3x3(a.x - b.x,
a.x - point.x,
direction.x,
a.y - b.y,
a.y - point.y,
direction.y,
a.z - b.z,
a.z - point.z,
direction.z
) / det

if (beta >= 0.0 && gamma >= 0.0 && beta + gamma <= 1.0) {
Expand Down Expand Up @@ -207,57 +208,3 @@ private[boundingSpheres] object BSIntersection {
}

}

private[boundingSpheres] object Determinantes {

@inline
def det2x2(a1: Double, a2: Double, b1: Double, b2: Double): Double = {
(+a1 * b2
- b1 * a2)
}

@inline
def det3x3(a1: Double, a2: Double, a3: Double, b1: Double, b2: Double, b3: Double, c1: Double, c2: Double, c3: Double)
: Double = {
(+a1 * det2x2(b2, b3, c2, c3)
- b1 * det2x2(a2, a3, c2, c3)
+ c1 * det2x2(a2, a3, b2, b3))
}

@inline
def det4x4(a1: Double,
a2: Double,
a3: Double,
a4: Double,
b1: Double,
b2: Double,
b3: Double,
b4: Double,
c1: Double,
c2: Double,
c3: Double,
c4: Double,
d1: Double,
d2: Double,
d3: Double,
d4: Double
): Double = {
(+a1 * det3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4)
- b1 * det3x3(c2, c3, c4, d2, d3, d4, a2, a3, a4)
+ c1 * det3x3(d2, d3, d4, a2, a3, a4, b2, b3, b4)
- d1 * det3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4)
- a2 * det3x3(b3, b4, b1, c3, c4, c1, d3, d4, d1)
+ b2 * det3x3(c3, c4, c1, d3, d4, d1, a3, a4, a1)
- c2 * det3x3(d3, d4, d1, a3, a4, a1, b3, b4, b1)
+ d2 * det3x3(a3, a4, a1, b3, b4, b1, c3, c4, c1)
+ a3 * det3x3(b4, b1, b2, c4, c1, c2, d4, d1, d2)
- b3 * det3x3(c4, c1, c2, d4, d1, d2, a4, a1, a2)
+ c3 * det3x3(d4, d1, d2, a4, a1, a2, b4, b1, b2)
- d3 * det3x3(a4, a1, a2, b4, b1, b2, c4, c1, c2)
- a4 * det3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3)
+ b4 * det3x3(c1, c2, c3, d1, d2, d3, a1, a2, a3)
- c4 * det3x3(d1, d2, d3, a1, a2, a3, b1, b2, b3)
+ d4 * det3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3))
}

}
54 changes: 54 additions & 0 deletions src/main/scala/scalismo/numerics/Determinant.scala
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Original file line number Diff line number Diff line change
@@ -0,0 +1,54 @@
package scalismo.numerics

object Determinant {

@inline
def det2x2(a1: Double, a2: Double, b1: Double, b2: Double): Double = {
(+a1 * b2
- b1 * a2)
}

@inline
def det3x3(a1: Double, a2: Double, a3: Double, b1: Double, b2: Double, b3: Double, c1: Double, c2: Double, c3: Double)
: Double = {
(+a1 * det2x2(b2, b3, c2, c3)
- b1 * det2x2(a2, a3, c2, c3)
+ c1 * det2x2(a2, a3, b2, b3))
}

@inline
def det4x4(a1: Double,
a2: Double,
a3: Double,
a4: Double,
b1: Double,
b2: Double,
b3: Double,
b4: Double,
c1: Double,
c2: Double,
c3: Double,
c4: Double,
d1: Double,
d2: Double,
d3: Double,
d4: Double
): Double = {
(+a1 * det3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4)
- b1 * det3x3(c2, c3, c4, d2, d3, d4, a2, a3, a4)
+ c1 * det3x3(d2, d3, d4, a2, a3, a4, b2, b3, b4)
- d1 * det3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4)
- a2 * det3x3(b3, b4, b1, c3, c4, c1, d3, d4, d1)
+ b2 * det3x3(c3, c4, c1, d3, d4, d1, a3, a4, a1)
- c2 * det3x3(d3, d4, d1, a3, a4, a1, b3, b4, b1)
+ d2 * det3x3(a3, a4, a1, b3, b4, b1, c3, c4, c1)
+ a3 * det3x3(b4, b1, b2, c4, c1, c2, d4, d1, d2)
- b3 * det3x3(c4, c1, c2, d4, d1, d2, a4, a1, a2)
+ c3 * det3x3(d4, d1, d2, a4, a1, a2, b4, b1, b2)
- d3 * det3x3(a4, a1, a2, b4, b1, b2, c4, c1, c2)
- a4 * det3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3)
+ b4 * det3x3(c1, c2, c3, d1, d2, d3, a1, a2, a3)
- c4 * det3x3(d1, d2, d3, a1, a2, a3, b1, b2, b3)
+ d4 * det3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3))
}
}