Ugh, sorry for the noise, first response had an attachment.
This is for a line and a box from code by David Eberly of Magic Software and
his #D Game engine book. Sorry, but a casual search for his web site is
coming up empty.
Function LineBoxIntersection(segment As LineSegment3D, box As Box3D) As
Boolean
// return value is 'true' if and only if objects intersect
// Clipping of a linear component 'origin'+t*'direction' against an
// axis-aligned box [-e0,e0]x[-e1,e1]x[-e2,e2] where 'extent'=(e0,e1,e2).
// The values of t0 and t1 must be set by the caller.
// If the component is a segment, set t0 = 0 and t1 = 1.
// The values are (possibly) modified by the clipper.
Dim AWdu(2),ADdu(2),AWxDdu(2), Rhs As Double
Dim sDirection, sCenter, Diff As Vector3D
sDirection = New Vector3D()
sDirection = segment.direction.Times(0.50)
sCenter = New Vector3D
sCenter = segment.origin.Plus(sDirection)
Diff = New Vector3D
Diff = sCenter.Minus(box.center) // tests requires a change
in the coord. system
// x
AWdu(0) = ABS(sDirection.Dot(box.axis(0)))
ADdu(0) = ABS(Diff.Dot(box.axis(0)))
Rhs = box.extent(0) + AWdu(0)
If ADdu(0) > Rhs Then
Return False
End
// y
AWdu(1) = ABS(sDirection.Dot(box.axis(1)))
ADdu(1) = ABS(Diff.Dot(box.axis(1)))
Rhs = box.extent(1) + AWdu(1)
If ADdu(1) > Rhs Then
Return False
End
// z
AWdu(2) = ABS(sDirection.Dot(box.axis(2)))
ADdu(2) = ABS(Diff.Dot(box.axis(2)))
Rhs = box.extent(2) + AWdu(2)
If ADdu(2) > Rhs Then
Return False
End
Dim WxD As Vector3D
WxD = sDirection.Cross(Diff)
//
AWxDdu(0) = ABS(WxD.Dot(box.axis(0)))
Rhs = box.extent(1) * AWdu(2) + box.extent(2) * AWdu(1)
if AWxDdu(0) > Rhs Then
Return False
End
//
AWxDdu(1) = ABS(WxD.Dot(box.axis(1)))
Rhs = box.extent(0) * AWdu(2) + box.extent(2) * AWdu(0)
if AWxDdu(1) > Rhs Then
Return False
End
//
AWxDdu(2) = ABS(WxD.Dot(box.axis(2)))
Rhs = box.extent(0) * AWdu(1) + box.extent(1) * AWdu(0)
if AWxDdu(2) > Rhs Then
Return False
End
//
Return True
End Function
LineSegment3D is a
direction As Vector3D
origin As Vector3D
Box3D is a
axis(2) As Vector3D
center As Vector3D
extent(2) As Double
Perhaps that would help you.
Thomas C.
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