1RTC_GEOMETRY_TYPE_*_CURVE(E3m)bree Ray Tracing KernelsRT4C_GEOMETRY_TYPE_*_CURVE(3)
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5   NAME
6              RTC_GEOMETRY_TYPE_FLAT_LINEAR_CURVE -
7                flat curve geometry with linear basis
8
9              RTC_GEOMETRY_TYPE_FLAT_BEZIER_CURVE -
10                flat curve geometry with cubic Bézier basis
11
12              RTC_GEOMETRY_TYPE_FLAT_BSPLINE_CURVE -
13                flat curve geometry with cubic B-spline basis
14
15              RTC_GEOMETRY_TYPE_FLAT_HERMITE_CURVE -
16                flat curve geometry with cubic Hermite basis
17
18              RTC_GEOMETRY_TYPE_FLAT_CATMULL_ROM_CURVE -
19                flat curve geometry with Catmull-Rom basis
20
21              RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_BEZIER_CURVE -
22                flat normal oriented curve geometry with cubic Bézier basis
23
24              RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_BSPLINE_CURVE -
25                flat normal oriented curve geometry with cubic B-spline basis
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27              RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_HERMITE_CURVE -
28                flat normal oriented curve geometry with cubic Hermite basis
29
30              RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_CATMULL_ROM_CURVE -
31                flat normal oriented curve geometry with Catmull-Rom basis
32
33              RTC_GEOMETRY_TYPE_CONE_LINEAR_CURVE -
34                capped cone curve geometry with linear basis - discontinuous at edge boundaries
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36              RTC_GEOMETRY_TYPE_ROUND_LINEAR_CURVE -
37                capped cone curve geometry with linear basis and spherical ending
38
39              RTC_GEOMETRY_TYPE_ROUND_BEZIER_CURVE -
40                swept surface curve geometry with cubic Bézier basis
41
42              RTC_GEOMETRY_TYPE_ROUND_BSPLINE_CURVE -
43                swept surface curve geometry with cubic B-spline basis
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45              RTC_GEOMETRY_TYPE_ROUND_HERMITE_CURVE -
46                swept surface curve geometry with cubic Hermite basis
47
48              RTC_GEOMETRY_TYPE_ROUND_CATMULL_ROM_CURVE -
49                swept surface curve geometry with Catmull-Rom basis
50
51   SYNOPSIS
52              #include <embree4/rtcore.h>
53
54              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_FLAT_LINEAR_CURVE);
55              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_FLAT_BEZIER_CURVE);
56              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_FLAT_BSPLINE_CURVE);
57              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_FLAT_HERMITE_CURVE);
58              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_FLAT_CATMULL_ROM_CURVE);
59              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_BEZIER_CURVE);
60              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_BSPLINE_CURVE);
61              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_HERMITE_CURVE);
62              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_CATMULL_ROM_CURVE);
63              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_CONE_LINEAR_CURVE);
64              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_ROUND_LINEAR_CURVE);
65              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_ROUND_BEZIER_CURVE);
66              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_ROUND_BSPLINE_CURVE);
67              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_ROUND_HERMITE_CURVE);
68              rtcNewGeometry(device, RTC_GEOMETRY_TYPE_ROUND_CATMULL_ROM_CURVE);
69
70   DESCRIPTION
71       Curves  with  per vertex radii are supported with linear, cubic Bézier,
72       cubic B-spline, and cubic Hermite bases.   Such  curve  geometries  are
73       created   by  passing  RTC_GEOMETRY_TYPE_FLAT_LINEAR_CURVE,  RTC_GEOME‐
74       TRY_TYPE_FLAT_BEZIER_CURVE,       RTC_GEOMETRY_TYPE_FLAT_BSPLINE_CURVE,
75       RTC_GEOMETRY_TYPE_FLAT_HERMITE_CURVE,       RTC_GEOMETRY_TYPE_FLAT_CAT‐
76       MULL_ROM_CURVE,    RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_FLAT_BEZIER_CURVE,
77       RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_FLAT_BSPLINE_CURVE,        RTC_GEOME‐
78       TRY_TYPE_NORMAL_ORIENTED_FLAT_HERMITE_CURVE,     RTC_GEOMETRY_TYPE_NOR‐
79       MAL_ORIENTED_FLAT_CATMULL_ROM_CURVE,        RTC_GEOMETRY_TYPE_CONE_LIN‐
80       EAR_CURVE,       RTC_GEOMETRY_TYPE_ROUND_LINEAR_CURVE,       RTC_GEOME‐
81       TRY_TYPE_ROUND_BEZIER_CURVE,     RTC_GEOMETRY_TYPE_ROUND_BSPLINE_CURVE,
82       RTC_GEOMETRY_TYPE_ROUND_HERMITE_CURVE, or  RTC_GEOMETRY_TYPE_ROUND_CAT‐
83       MULL_ROM_CURVE  to  the rtcNewGeometry function.  The curve indices can
84       be specified through an index buffer  (RTC_BUFFER_TYPE_INDEX)  and  the
85       curve  vertices  through a vertex buffer (RTC_BUFFER_TYPE_VERTEX).  For
86       the Hermite basis a tangent  buffer  (RTC_BUFFER_TYPE_TANGENT),  normal
87       oriented  curves a normal buffer (RTC_BUFFER_TYPE_NORMAL), and for nor‐
88       mal oriented  Hermite  curves  a  normal  derivative  buffer  (RTC_BUF‐
89       FER_TYPE_NORMAL_DERIVATIVE)  has  to  get  specified additionally.  See
90       rtcSetGeometryBuffer and rtcSetSharedGeometryBuffer for more details on
91       how to set buffers.
92
93       The  index  buffer contains an array of 32-bit indices (RTC_FORMAT_UINT
94       format), each pointing to the first control vertex in the  vertex  buf‐
95       fer,  but  also  to  the first tangent in the tangent buffer, and first
96       normal in the normal buffer if these buffers are present.
97
98       The vertex buffer stores each control vertex in the form  of  a  single
99       precision  position  and  radius stored in (x, y, z, r) order in memory
100       (RTC_FORMAT_FLOAT4 format).  The number of vertices  is  inferred  from
101       the  size  of  this buffer.  The radii may be smaller than zero but the
102       interpolated radii should always be greater or equal to zero.  Similar‐
103       ly, the tangent buffer stores the derivative of each control vertex (x,
104       y, z, r order and  RTC_FORMAT_FLOAT4  format)  and  the  normal  buffer
105       stores  a single precision normal per control vertex (x, y, z order and
106       RTC_FORMAT_FLOAT3 format).
107
108   Linear Basis
109       For the linear basis the indices point to the first  of  2  consecutive
110       control  points  in  the vertex buffer.  The first control point is the
111       start and the second control point the end of the line  segment.   When
112       constructing  hair  strands  in this basis, the end-point can be shared
113       with the start of the next line segment.
114
115       For the linear basis the user optionally can provide a flags buffer  of
116       type RTC_BUFFER_TYPE_FLAGS which contains bytes that encode if the left
117       neighbor  segment  (RTC_CURVE_FLAG_NEIGHBOR_LEFT  flag)  and/or   right
118       neighbor segment (RTC_CURVE_FLAG_NEIGHBOR_RIGHT flags) exist (see [RTC‐
119       CurveFlags]).  If this buffer is not set, than the left/right  neighbor
120       bits  are  automatically calculated base on the index buffer (left seg‐
121       ment exists if segment(id-1)+1 == segment(id) and right segment  exists
122       if segment(id+1)-1 == segment(id)).
123
124       A  left  neighbor  segment is assumed to end at the start vertex of the
125       current segment, and to start at the previous vertex in the vertex buf‐
126       fer.   Similarly, the right neighbor segment is assumed to start at the
127       end vertex of the current segment, and to end at the next vertex in the
128       vertex buffer.
129
130       Only  when  the  left and right bits are properly specified the current
131       segment can properly attach to the left and/or right  neighbor,  other‐
132       wise the touching area may not get rendered properly.
133
134   Bézier Basis
135       For the cubic Bézier basis the indices point to the first of 4 consecu‐
136       tive control points in the vertex buffer.  These control points use the
137       cubic  Bézier basis, where the first control point represents the start
138       point of the curve, and the 4th control point  the  end  point  of  the
139       curve.   The  Bézier basis is interpolating, thus the curve does go ex‐
140       actly through the first and fourth control vertex.
141
142   B-spline Basis
143       For the cubic B-spline basis the indices point to the first of  4  con‐
144       secutive  control  points  in  the vertex buffer.  These control points
145       make up a cardinal cubic B-spline (implicit equidistant  knot  vector).
146       This  basis is not interpolating, thus the curve does in general not go
147       through any of the control points directly.  A big  advantage  of  this
148       basis  is that 3 control points can be shared for two continuous neigh‐
149       boring curve segments, e.g. the curves (p0,p1,p2,p3) and  (p1,p2,p3,p4)
150       are C1 continuous.  This feature makes this basis a good choice to con‐
151       struct continuous multi-segment curves, as memory  consumption  can  be
152       kept minimal.
153
154   Hermite Basis
155       For the cubic Hermite basis the indices point to the first of 2 consec‐
156       utive points in the vertex buffer, and the first of 2 consecutive  tan‐
157       gents in the tangent buffer.  These two points and two tangents make up
158       a cubic Hermite curve.  This basis is interpolating, thus does  exactly
159       go  through the first and second control point, and the first order de‐
160       rivative at the begin and end matches exactly the  value  specified  in
161       the tangent buffer.  When connecting two segments continuously, the end
162       point and tangent of the previous segment  can  be  shared.   Different
163       versions  of  Catmull-Rom  splines  can be easily constructed using the
164       Hermite basis, by calculating a proper tangent buffer from the  control
165       points.
166
167   Catmull-Rom Basis
168       For  the Catmull-Rom basis the indices point to the first of 4 consecu‐
169       tive control points in the vertex buffer.  This basis goes  through  p1
170       and p2, with tangents (p2-p0)/2 and (p3-p1)/2.
171
172   Flat Curves
173       The  RTC_GEOMETRY_TYPE_FLAT_* flat mode is a fast mode designed to ren‐
174       der distant hair.  In this mode the curve is rendered  as  a  connected
175       sequence  of ray facing quads.  Individual quads are considered to have
176       subpixel size, and zooming onto the curve might  show  geometric  arti‐
177       facts.   The number of quads to subdivide into can be specified through
178       the rtcSetGeometryTessellationRate function.  By default the  tessella‐
179       tion rate is 4.
180
181   Normal Oriented Curves
182       The RTC_GEOMETRY_TYPE_NORMAL_ORIENTED_* mode is a mode designed to ren‐
183       der blades of grass.  In this mode a vertex spline has to get specified
184       as  for  the  previous  modes,  but additionally a normal spline is re‐
185       quired.  If the Hermite basis is used, the  RTC_BUFFER_TYPE_NORMAL  and
186       RTC_BUFFER_TYPE_NORMAL_DERIVATIVE buffers have both to be set.
187
188       The curve is rendered as a flat band whose center approximately follows
189       the provided vertex spline, whose half width approximately follows  the
190       provided radius spline, and whose normal orientation approximately fol‐
191       lows the provided normal spline.
192
193       To intersect the normal oriented curve,  we  perform  a  newton-raphson
194       style  intersection  of a ray with a tensor product surface of a linear
195       basis (perpendicular to the curve) and cubic Bézier  basis  (along  the
196       curve).  We use a guide curve and its derivatives to construct the con‐
197       trol points of that surface.  The guide curve is  defined  by  a  sweep
198       surface  defined by sweeping a line centered at the vertex spline loca‐
199       tion along the curve.  At each parameter value the half  width  of  the
200       line  matches  the  radius  spline, and the direction matches the cross
201       product of the normal from the normal spline and tangent of the  vertex
202       spline.   Note  that  this construction does not work when the provided
203       normals are parallel to the curve direction.  For this reason the  pro‐
204       vided  normals should best be kept as perpendicular to the curve direc‐
205       tion as possible.  We further assume second order  derivatives  of  the
206       center  curve to be zero for this construction, as otherwise very large
207       curvatures occurring in corner cases, can thicken the constructed curve
208       significantly.
209
210   Round Curves
211       In  the  RTC_GEOMETRY_TYPE_ROUND_* round mode, a real geometric surface
212       is rendered for the curve, which is more expensive but  allows  closeup
213       views.
214
215       For  the  linear  basis the round mode renders a cone that tangentially
216       touches a start-sphere and end-sphere.  The start  sphere  is  rendered
217       when  no  previous segments is indicated by the neighbor bits.  The end
218       sphere is always rendered but parts that lie inside  the  next  segment
219       are  clipped  away  (if that next segment exists).  This way a curve is
220       closed on both ends and the interior will render properly  as  long  as
221       only  neighboring  segments penetrate into a segment.  For this to work
222       properly it is important that the flags buffer  is  properly  populated
223       with neighbor information.
224
225       For  the cubic polynomial bases, the round mode renders a sweep surface
226       by sweeping a varying radius circle tangential along the curve.   As  a
227       limitation,  the  radius of the curve has to be smaller than the curva‐
228       ture radius of the curve at each location on the curve.
229
230       The intersection with the curve segment stores the parametric hit loca‐
231       tion along the curve segment as u-coordinate (range 0 to +1).
232
233       For  flat curves, the v-coordinate is set to the normalized distance in
234       the range -1 to +1.  For normal oriented curves the v-coordinate is  in
235       the range 0 to 1.  For the linear basis and in round mode the v-coordi‐
236       nate is set to zero.
237
238       In flat mode, the geometry normal Ng is set to the tangent of the curve
239       at the hit location.  In round mode and for normal oriented curves, the
240       geometry normal Ng is set to the non-normalized geometric normal of the
241       surface.
242
243       For  multi-segment  motion blur, the number of time steps must be first
244       specified using the rtcSetGeometryTimeStepCount call.   Then  a  vertex
245       buffer  for each time step can be set using different buffer slots, and
246       all these buffers must have the same stride and size.  For the  Hermite
247       basis  also  a  tangent buffer has to be set for each time step and for
248       normal oriented curves a normal buffer has to get  specified  for  each
249       time step.
250
251       Also  see  tutorials  [Hair] and [Curves] for examples of how to create
252       and use curve geometries.
253
254   EXIT STATUS
255       On failure NULL is returned and an  error  code  is  set  that  can  be
256       queried using rtcGetDeviceError.
257
258   SEE ALSO
259       [rtcNewGeometry], [RTCCurveFlags]
260
261
262
263                                                  RTC_GEOMETRY_TYPE_*_CURVE(3)
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