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.TH "RTC_GEOMETRY_TYPE_*_CURVE" "3" "" "" "Embree Ray Tracing Kernels 3"
.hy
.SS NAME
.IP
.nf
\f[C]
RTC_GEOMETRY_TYPE_FLAT_LINEAR_CURVE \-
  flat curve geometry with linear basis

RTC_GEOMETRY_TYPE_FLAT_BEZIER_CURVE \-
  flat curve geometry with cubic B\['e]zier basis

RTC_GEOMETRY_TYPE_FLAT_BSPLINE_CURVE \- 
  flat curve geometry with cubic B\-spline basis

RTC_GEOMETRY_TYPE_FLAT_HERMITE_CURVE \- 
  flat curve geometry with cubic Hermite basis

RTC_GEOMETRY_TYPE_FLAT_CATMULL_ROM_CURVE \- 
  flat curve geometry with Catmull\-Rom basis

RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_BEZIER_CURVE \-
  flat normal oriented curve geometry with cubic B\['e]zier basis

RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_BSPLINE_CURVE \- 
  flat normal oriented curve geometry with cubic B\-spline basis

RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_HERMITE_CURVE \- 
  flat normal oriented curve geometry with cubic Hermite basis

RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_CATMULL_ROM_CURVE \- 
  flat normal oriented curve geometry with Catmull\-Rom basis

RTC_GEOMETRY_TYPE_CONE_LINEAR_CURVE \-
  capped cone curve geometry with linear basis \- discontinous at edge boundaries

RTC_GEOMETRY_TYPE_ROUND_LINEAR_CURVE \-
  capped cone curve geometry with linear basis and spherical ending

RTC_GEOMETRY_TYPE_ROUND_BEZIER_CURVE \-
  swept surface curve geometry with cubic B\['e]zier basis

RTC_GEOMETRY_TYPE_ROUND_BSPLINE_CURVE \-
  swept surface curve geometry with cubic B\-spline basis

RTC_GEOMETRY_TYPE_ROUND_HERMITE_CURVE \-
  swept surface curve geometry with cubic Hermite basis

RTC_GEOMETRY_TYPE_ROUND_CATMULL_ROM_CURVE \-
  swept surface curve geometry with Catmull\-Rom basis
\f[R]
.fi
.SS SYNOPSIS
.IP
.nf
\f[C]
#include <embree3/rtcore.h>

rtcNewGeometry(device, RTC_GEOMETRY_TYPE_FLAT_LINEAR_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_FLAT_BEZIER_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_FLAT_BSPLINE_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_FLAT_HERMITE_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_FLAT_CATMULL_ROM_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_BEZIER_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_BSPLINE_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_HERMITE_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_CATMULL_ROM_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_CONE_LINEAR_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_ROUND_LINEAR_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_ROUND_BEZIER_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_ROUND_BSPLINE_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_ROUND_HERMITE_CURVE);
rtcNewGeometry(device, RTC_GEOMETRY_TYPE_ROUND_CATMULL_ROM_CURVE);
\f[R]
.fi
.SS DESCRIPTION
.PP
Curves with per vertex radii are supported with linear, cubic
B\['e]zier, cubic B\-spline, and cubic Hermite bases.
Such curve geometries are created by passing
\f[C]RTC_GEOMETRY_TYPE_FLAT_LINEAR_CURVE\f[R],
\f[C]RTC_GEOMETRY_TYPE_FLAT_BEZIER_CURVE\f[R],
\f[C]RTC_GEOMETRY_TYPE_FLAT_BSPLINE_CURVE\f[R],
\f[C]RTC_GEOMETRY_TYPE_FLAT_HERMITE_CURVE\f[R],
\f[C]RTC_GEOMETRY_TYPE_FLAT_CATMULL_ROM_CURVE\f[R],
\f[C]RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_FLAT_BEZIER_CURVE\f[R],
\f[C]RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_FLAT_BSPLINE_CURVE\f[R],
\f[C]RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_FLAT_HERMITE_CURVE\f[R],
\f[C]RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_FLAT_CATMULL_ROM_CURVE\f[R],
\f[C]RTC_GEOMETRY_TYPE_CONE_LINEAR_CURVE\f[R],
\f[C]RTC_GEOMETRY_TYPE_ROUND_LINEAR_CURVE\f[R],
\f[C]RTC_GEOMETRY_TYPE_ROUND_BEZIER_CURVE\f[R],
\f[C]RTC_GEOMETRY_TYPE_ROUND_BSPLINE_CURVE\f[R],
\f[C]RTC_GEOMETRY_TYPE_ROUND_HERMITE_CURVE\f[R], or
\f[C]RTC_GEOMETRY_TYPE_ROUND_CATMULL_ROM_CURVE\f[R] to the
\f[C]rtcNewGeometry\f[R] function.
The curve indices can be specified through an index buffer
(\f[C]RTC_BUFFER_TYPE_INDEX\f[R]) and the curve vertices through a
vertex buffer (\f[C]RTC_BUFFER_TYPE_VERTEX\f[R]).
For the Hermite basis a tangent buffer
(\f[C]RTC_BUFFER_TYPE_TANGENT\f[R]), normal oriented curves a normal
buffer (\f[C]RTC_BUFFER_TYPE_NORMAL\f[R]), and for normal oriented
Hermite curves a normal derivative buffer
(\f[C]RTC_BUFFER_TYPE_NORMAL_DERIVATIVE\f[R]) has to get specified
additionally.
See \f[C]rtcSetGeometryBuffer\f[R] and
\f[C]rtcSetSharedGeometryBuffer\f[R] for more details on how to set
buffers.
.PP
The index buffer contains an array of 32\-bit indices
(\f[C]RTC_FORMAT_UINT\f[R] format), each pointing to the first control
vertex in the vertex buffer, but also to the first tangent in the
tangent buffer, and first normal in the normal buffer if these buffers
are present.
.PP
The vertex buffer stores each control vertex in the form of a single
precision position and radius stored in (\f[C]x\f[R], \f[C]y\f[R],
\f[C]z\f[R], \f[C]r\f[R]) order in memory (\f[C]RTC_FORMAT_FLOAT4\f[R]
format).
The number of vertices is inferred from the size of this buffer.
The radii may be smaller than zero but the interpolated radii should
always be greater or equal to zero.
Similarly, the tangent buffer stores the derivative of each control
vertex (\f[C]x\f[R], \f[C]y\f[R], \f[C]z\f[R], \f[C]r\f[R] order and
\f[C]RTC_FORMAT_FLOAT4\f[R] format) and the normal buffer stores a
single precision normal per control vertex (\f[C]x\f[R], \f[C]y\f[R],
\f[C]z\f[R] order and \f[C]RTC_FORMAT_FLOAT3\f[R] format).
.SS Linear Basis
.PP
For the linear basis the indices point to the first of 2 consecutive
control points in the vertex buffer.
The first control point is the start and the second control point the
end of the line segment.
When constructing hair strands in this basis, the end\-point can be
shared with the start of the next line segment.
.PP
For the linear basis the user optionally can provide a flags buffer of
type \f[C]RTC_BUFFER_TYPE_FLAGS\f[R] which contains bytes that encode if
the left neighbor segment (\f[C]RTC_CURVE_FLAG_NEIGHBOR_LEFT\f[R] flag)
and/or right neighbor segment (\f[C]RTC_CURVE_FLAG_NEIGHBOR_RIGHT\f[R]
flags) exist (see [RTCCurveFlags]).
If this buffer is not set, than the left/right neighbor bits are
automatically calculated base on the index buffer (left segment exists
if segment(id\-1)+1 == segment(id) and right segment exists if
segment(id+1)\-1 == segment(id)).
.PP
A left neighbor segment is assumed to end at the start vertex of the
current segement, and to start at the previous vertex in the vertex
buffer.
Similarly, the right neighbor segment is assumed to start at the end
vertex of the current segment, and to end at the next vertex in the
vertex buffer.
.PP
Only when the left and right bits are properly specified the current
segment can properly attach to the left and/or right neighbor, otherwise
the touching area may not get rendererd properly.
.SS B\['e]zier Basis
.PP
For the cubic B\['e]zier basis the indices point to the first of 4
consecutive control points in the vertex buffer.
These control points use the cubic B\['e]zier basis, where the first
control point represents the start point of the curve, and the 4th
control point the end point of the curve.
The B\['e]zier basis is interpolating, thus the curve does go exactly
through the first and fourth control vertex.
.SS B\-spline Basis
.PP
For the cubic B\-spline basis the indices point to the first of 4
consecutive control points in the vertex buffer.
These control points make up a cardinal cubic B\-spline (implicit
equidistant knot vector).
This basis is not interpolating, thus the curve does in general not go
through any of the control points directly.
A big advantage of this basis is that 3 control points can be shared for
two continuous neighboring curve segments, e.g.\ the curves
(p0,p1,p2,p3) and (p1,p2,p3,p4) are C1 continuous.
This feature make this basis a good choise to construct continuous
multi\-segment curves, as memory consumption can be kept minimal.
.SS Hermite Basis
.PP
For the cubic Hermite basis the indices point to the first of 2
consecutive points in the vertex buffer, and the first of 2 consecutive
tangents in the tangent buffer.
These two points and two tangents make up a cubic Hermite curve.
This basis is interpolating, thus does exactly go through the first and
second control point, and the first order derivative at the begin and
end matches exactly the value specified in the tangent buffer.
When connecting two segments continuously, the end point and tangent of
the previous segment can be shared.
Different versions of Catmull\-Rom splines can be easily constructed
usig the Hermite basis, by calculating a proper tangent buffer from the
control points.
.SS Catmull\-Rom Basis
.PP
For the Catmull\-Rom basis the indices point to the first of 4
consecutive control points in the vertex buffer.
This basis goes through p1 and p2, with tangents (p2\-p0)/2 and
(p3\-p1)/2.
.SS Flat Curves
.PP
The \f[C]RTC_GEOMETRY_TYPE_FLAT_*\f[R] flat mode is a fast mode designed
to render distant hair.
In this mode the curve is rendered as a connected sequence of ray facing
quads.
Individual quads are considered to have subpixel size, and zooming onto
the curve might show geometric artifacts.
The number of quads to subdivide into can be specified through the
\f[C]rtcSetGeometryTessellationRate\f[R] function.
By default the tessellation rate is 4.
.SS Normal Oriented Curves
.PP
The \f[C]RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_*\f[R] mode is a mode
designed to render blades of grass.
In this mode a vertex spline has to get specified as for the previous
modes, but additionally a normal spline is required.
If the Hermite basis is used, the \f[C]RTC_BUFFER_TYPE_NORMAL\f[R] and
\f[C]RTC_BUFFER_TYPE_NORMAL_DERIVATIVE\f[R] buffers have both to be set.
.PP
The curve is rendered as a flat band whose center approximately follows
the provided vertex spline, whose half width approximately follows the
provided radius spline, and whose normal orientation approximately
follows the provided normal spline.
.PP
To intersect the normal oriented curve, we perform a newton\-raphson
style intersection of a ray with a tensor product surface of a linear
basis (perpendicular to the curve) and cubic B\['e]zier basis (along the
curve).
We use a guide curve and its derivatives to construct the control points
of that surface.
The guide curve is defined by a sweep surface defined by sweeping a line
centered at the vertex spline location along the curve.
At each parameter value the half width of the line matches the radius
spline, and the direction matches the cross product of the normal from
the normal spline and tangent of the vertex spline.
Note that this construction does not work when the provided normals are
parallel to the curve direction.
For this reason the provided normals should best be kept as
perpendicular to the curve direction as possible.
.SS Round Curves
.PP
In the \f[C]RTC_GEOMETRY_TYPE_ROUND_*\f[R] round mode, a real geometric
surface is rendered for the curve, which is more expensive but allows
closeup views.
.PP
For the linear basis the round mode renders a cone that tangentially
touches a start\-sphere and end\-sphere.
The start sphere is rendered when no previous segments is indicated by
the neighbor bits.
The end sphere is always rendered but parts that lie inside the next
segment are clipped away (if that next segment exists).
This way a curve is closed on both ends and the interiour will render
properly as long as only neighboring segments penetrate into a segment.
For this to work properly it is important that the flags buffer is
properly populated with neighbor information.
.PP
For the cubic polynomial bases, the round mode renders a sweep surface
by sweeping a varying radius circle tangential along the curve.
As a limitation, the radius of the curve has to be smaller than the
curvature radius of the curve at each location on the curve.
.PP
The intersection with the curve segment stores the parametric hit
location along the curve segment as u\-coordinate (range 0 to +1).
.PP
For flat curves, the v\-coordinate is set to the normalized distance in
the range \-1 to +1.
For normal oriented curves the v\-coordinate is in the range 0 to 1.
For the linear basis and in round mode the v\-coordinate is set to zero.
.PP
In flat mode, the geometry normal \f[C]Ng\f[R] is set to the tangent of
the curve at the hit location.
In round mode and for normal oriented curves, the geometry normal
\f[C]Ng\f[R] is set to the non\-normalized geometric normal of the
surface.
.PP
For multi\-segment motion blur, the number of time steps must be first
specified using the \f[C]rtcSetGeometryTimeStepCount\f[R] call.
Then a vertex buffer for each time step can be set using different
buffer slots, and all these buffers must have the same stride and size.
For the Hermite basis also a tangent buffer has to be set for each time
step and for normal oriented curves a normal buffer has to get specified
for each time step.
.PP
Also see tutorials [Hair] and [Curves] for examples of how to create and
use curve geometries.
.SS EXIT STATUS
.PP
On failure \f[C]NULL\f[R] is returned and an error code is set that can
be queried using \f[C]rtcGetDeviceError\f[R].
.SS SEE ALSO
.PP
[rtcNewGeometry], [RTCCurveFlags]
