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><H1
><A
NAME="GTS-DIFFERENTIAL-GEOMETRY-OPERATORS"
></A
>Differential geometry operators</H1
><DIV
CLASS="REFNAMEDIV"
><A
NAME="AEN15040"
></A
><H2
>Name</H2
>Differential geometry operators -- </DIV
><DIV
CLASS="REFSYNOPSISDIV"
><A
NAME="AEN15043"
></A
><H2
>Synopsis</H2
><PRE
CLASS="SYNOPSIS"
> #include <gts.h>
<GTKDOCLINK
HREF="GBOOLEAN"
>gboolean</GTKDOCLINK
> <A
HREF="gts-differential-geometry-operators.html#GTS-VERTEX-GAUSSIAN-CURVATURE"
>gts_vertex_gaussian_curvature</A
> (<A
HREF="gts-vertices.html#GTSVERTEX"
>GtsVertex</A
> *v,
<A
HREF="gts-surfaces.html#GTSSURFACE"
>GtsSurface</A
> *s,
<GTKDOCLINK
HREF="GDOUBLE"
>gdouble</GTKDOCLINK
> *Kg);
<GTKDOCLINK
HREF="GBOOLEAN"
>gboolean</GTKDOCLINK
> <A
HREF="gts-differential-geometry-operators.html#GTS-VERTEX-MEAN-CURVATURE-NORMAL"
>gts_vertex_mean_curvature_normal</A
>
(<A
HREF="gts-vertices.html#GTSVERTEX"
>GtsVertex</A
> *v,
<A
HREF="gts-surfaces.html#GTSSURFACE"
>GtsSurface</A
> *s,
<GTKDOCLINK
HREF="GTSVECTOR"
>GtsVector</GTKDOCLINK
> Kh);
<GTKDOCLINK
HREF="VOID"
>void</GTKDOCLINK
> <A
HREF="gts-differential-geometry-operators.html#GTS-VERTEX-PRINCIPAL-CURVATURES"
>gts_vertex_principal_curvatures</A
> (<GTKDOCLINK
HREF="GDOUBLE"
>gdouble</GTKDOCLINK
> Kh,
<GTKDOCLINK
HREF="GDOUBLE"
>gdouble</GTKDOCLINK
> Kg,
<GTKDOCLINK
HREF="GDOUBLE"
>gdouble</GTKDOCLINK
> *K1,
<GTKDOCLINK
HREF="GDOUBLE"
>gdouble</GTKDOCLINK
> *K2);
<GTKDOCLINK
HREF="VOID"
>void</GTKDOCLINK
> <A
HREF="gts-differential-geometry-operators.html#GTS-VERTEX-PRINCIPAL-DIRECTIONS"
>gts_vertex_principal_directions</A
> (<A
HREF="gts-vertices.html#GTSVERTEX"
>GtsVertex</A
> *v,
<A
HREF="gts-surfaces.html#GTSSURFACE"
>GtsSurface</A
> *s,
<GTKDOCLINK
HREF="GTSVECTOR"
>GtsVector</GTKDOCLINK
> Kh,
<GTKDOCLINK
HREF="GDOUBLE"
>gdouble</GTKDOCLINK
> Kg,
<GTKDOCLINK
HREF="GTSVECTOR"
>GtsVector</GTKDOCLINK
> e1,
<GTKDOCLINK
HREF="GTSVECTOR"
>GtsVector</GTKDOCLINK
> e2);</PRE
></DIV
><DIV
CLASS="REFSECT1"
><A
NAME="AEN15070"
></A
><H2
>Description</H2
><P
></P
></DIV
><DIV
CLASS="REFSECT1"
><A
NAME="AEN15073"
></A
><H2
>Details</H2
><DIV
CLASS="REFSECT2"
><A
NAME="AEN15075"
></A
><H3
><A
NAME="GTS-VERTEX-GAUSSIAN-CURVATURE"
></A
>gts_vertex_gaussian_curvature ()</H3
><PRE
CLASS="PROGRAMLISTING"
><GTKDOCLINK
HREF="GBOOLEAN"
>gboolean</GTKDOCLINK
> gts_vertex_gaussian_curvature (<A
HREF="gts-vertices.html#GTSVERTEX"
>GtsVertex</A
> *v,
<A
HREF="gts-surfaces.html#GTSSURFACE"
>GtsSurface</A
> *s,
<GTKDOCLINK
HREF="GDOUBLE"
>gdouble</GTKDOCLINK
> *Kg);</PRE
><P
>Computes the Discrete Gaussian Curvature approximation at <CODE
CLASS="PARAMETER"
>v</CODE
>.</P
><P
>This approximation is from the paper:
Discrete Differential-Geometry Operators for Triangulated 2-Manifolds
Mark Meyer, Mathieu Desbrun, Peter Schroder, Alan H. Barr
VisMath '02, Berlin (Germany)
http://www-grail.usc.edu/pubs.html</P
><P
></P
><P
></P
><TABLE
CLASS="variablelist"
BORDER="0"
CELLSPACING="0"
CELLPADDING="4"
><TBODY
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15090"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>v</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> a <A
HREF="gts-vertices.html#GTSVERTEX"
><SPAN
CLASS="TYPE"
>GtsVertex</SPAN
></A
>. </P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15097"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>s</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> a <A
HREF="gts-surfaces.html#GTSSURFACE"
><SPAN
CLASS="TYPE"
>GtsSurface</SPAN
></A
>.</P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15104"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>Kg</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> the Discrete Gaussian Curvature approximation at <CODE
CLASS="PARAMETER"
>v</CODE
>.</P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15110"><SPAN
STYLE="white-space: nowrap"
><SPAN
CLASS="emphasis"
><I
CLASS="EMPHASIS"
>Returns</I
></SPAN
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> <TT
CLASS="LITERAL"
>TRUE</TT
> if the operator could be evaluated, <TT
CLASS="LITERAL"
>FALSE</TT
> if the
evaluation failed for some reason (<CODE
CLASS="PARAMETER"
>v</CODE
> is boundary or is the
endpoint of a non-manifold edge.)</P
></TD
></TR
></TBODY
></TABLE
></DIV
><HR><DIV
CLASS="REFSECT2"
><A
NAME="AEN15118"
></A
><H3
><A
NAME="GTS-VERTEX-MEAN-CURVATURE-NORMAL"
></A
>gts_vertex_mean_curvature_normal ()</H3
><PRE
CLASS="PROGRAMLISTING"
><GTKDOCLINK
HREF="GBOOLEAN"
>gboolean</GTKDOCLINK
> gts_vertex_mean_curvature_normal
(<A
HREF="gts-vertices.html#GTSVERTEX"
>GtsVertex</A
> *v,
<A
HREF="gts-surfaces.html#GTSSURFACE"
>GtsSurface</A
> *s,
<GTKDOCLINK
HREF="GTSVECTOR"
>GtsVector</GTKDOCLINK
> Kh);</PRE
><P
>Computes the Discrete Mean Curvature Normal approximation at <CODE
CLASS="PARAMETER"
>v</CODE
>.
The mean curvature at <CODE
CLASS="PARAMETER"
>v</CODE
> is half the magnitude of the vector <CODE
CLASS="PARAMETER"
>Kh</CODE
>.</P
><P
>Note: the normal computed is not unit length, and may point either
into or out of the surface, depending on the curvature at <CODE
CLASS="PARAMETER"
>v</CODE
>. It
is the responsibility of the caller of the function to use the mean
curvature normal appropriately.</P
><P
>This approximation is from the paper:
Discrete Differential-Geometry Operators for Triangulated 2-Manifolds
Mark Meyer, Mathieu Desbrun, Peter Schroder, Alan H. Barr
VisMath '02, Berlin (Germany)
http://www-grail.usc.edu/pubs.html</P
><P
></P
><P
></P
><TABLE
CLASS="variablelist"
BORDER="0"
CELLSPACING="0"
CELLPADDING="4"
><TBODY
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15137"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>v</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> a <A
HREF="gts-vertices.html#GTSVERTEX"
><SPAN
CLASS="TYPE"
>GtsVertex</SPAN
></A
>. </P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15144"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>s</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> a <A
HREF="gts-surfaces.html#GTSSURFACE"
><SPAN
CLASS="TYPE"
>GtsSurface</SPAN
></A
>.</P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15151"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>Kh</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> the Mean Curvature Normal at <CODE
CLASS="PARAMETER"
>v</CODE
>.</P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15157"><SPAN
STYLE="white-space: nowrap"
><SPAN
CLASS="emphasis"
><I
CLASS="EMPHASIS"
>Returns</I
></SPAN
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> <TT
CLASS="LITERAL"
>TRUE</TT
> if the operator could be evaluated, <TT
CLASS="LITERAL"
>FALSE</TT
> if the
evaluation failed for some reason (<CODE
CLASS="PARAMETER"
>v</CODE
> is boundary or is the
endpoint of a non-manifold edge.)</P
></TD
></TR
></TBODY
></TABLE
></DIV
><HR><DIV
CLASS="REFSECT2"
><A
NAME="AEN15165"
></A
><H3
><A
NAME="GTS-VERTEX-PRINCIPAL-CURVATURES"
></A
>gts_vertex_principal_curvatures ()</H3
><PRE
CLASS="PROGRAMLISTING"
><GTKDOCLINK
HREF="VOID"
>void</GTKDOCLINK
> gts_vertex_principal_curvatures (<GTKDOCLINK
HREF="GDOUBLE"
>gdouble</GTKDOCLINK
> Kh,
<GTKDOCLINK
HREF="GDOUBLE"
>gdouble</GTKDOCLINK
> Kg,
<GTKDOCLINK
HREF="GDOUBLE"
>gdouble</GTKDOCLINK
> *K1,
<GTKDOCLINK
HREF="GDOUBLE"
>gdouble</GTKDOCLINK
> *K2);</PRE
><P
>Computes the principal curvatures at a point given the mean and
Gaussian curvatures at that point. </P
><P
>The mean curvature can be computed as one-half the magnitude of the
vector computed by <A
HREF="gts-differential-geometry-operators.html#GTS-VERTEX-MEAN-CURVATURE-NORMAL"
><CODE
CLASS="FUNCTION"
>gts_vertex_mean_curvature_normal()</CODE
></A
>.</P
><P
>The Gaussian curvature can be computed with
<A
HREF="gts-differential-geometry-operators.html#GTS-VERTEX-GAUSSIAN-CURVATURE"
><CODE
CLASS="FUNCTION"
>gts_vertex_gaussian_curvature()</CODE
></A
>.</P
><P
></P
><P
></P
><TABLE
CLASS="variablelist"
BORDER="0"
CELLSPACING="0"
CELLPADDING="4"
><TBODY
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15185"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>Kh</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> mean curvature.</P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15190"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>Kg</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> Gaussian curvature.</P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15195"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>K1</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> first principal curvature.</P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15200"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>K2</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> second principal curvature.</P
></TD
></TR
></TBODY
></TABLE
></DIV
><HR><DIV
CLASS="REFSECT2"
><A
NAME="AEN15205"
></A
><H3
><A
NAME="GTS-VERTEX-PRINCIPAL-DIRECTIONS"
></A
>gts_vertex_principal_directions ()</H3
><PRE
CLASS="PROGRAMLISTING"
><GTKDOCLINK
HREF="VOID"
>void</GTKDOCLINK
> gts_vertex_principal_directions (<A
HREF="gts-vertices.html#GTSVERTEX"
>GtsVertex</A
> *v,
<A
HREF="gts-surfaces.html#GTSSURFACE"
>GtsSurface</A
> *s,
<GTKDOCLINK
HREF="GTSVECTOR"
>GtsVector</GTKDOCLINK
> Kh,
<GTKDOCLINK
HREF="GDOUBLE"
>gdouble</GTKDOCLINK
> Kg,
<GTKDOCLINK
HREF="GTSVECTOR"
>GtsVector</GTKDOCLINK
> e1,
<GTKDOCLINK
HREF="GTSVECTOR"
>GtsVector</GTKDOCLINK
> e2);</PRE
><P
>Computes the principal curvature directions at a point given <CODE
CLASS="PARAMETER"
>Kh</CODE
>
and <CODE
CLASS="PARAMETER"
>Kg</CODE
>, the mean curvature normal and Gaussian curvatures at that
point, computed with <A
HREF="gts-differential-geometry-operators.html#GTS-VERTEX-MEAN-CURVATURE-NORMAL"
><CODE
CLASS="FUNCTION"
>gts_vertex_mean_curvature_normal()</CODE
></A
> and
<A
HREF="gts-differential-geometry-operators.html#GTS-VERTEX-GAUSSIAN-CURVATURE"
><CODE
CLASS="FUNCTION"
>gts_vertex_gaussian_curvature()</CODE
></A
>, respectively. </P
><P
>Note that this computation is very approximate and tends to be
unstable. Smoothing of the surface or the principal directions may
be necessary to achieve reasonable results.</P
><P
></P
><P
></P
><TABLE
CLASS="variablelist"
BORDER="0"
CELLSPACING="0"
CELLPADDING="4"
><TBODY
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15228"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>v</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> a <A
HREF="gts-vertices.html#GTSVERTEX"
><SPAN
CLASS="TYPE"
>GtsVertex</SPAN
></A
>. </P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15235"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>s</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> a <A
HREF="gts-surfaces.html#GTSSURFACE"
><SPAN
CLASS="TYPE"
>GtsSurface</SPAN
></A
>.</P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15242"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>Kh</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> mean curvature normal (a <GTKDOCLINK
HREF="GTSVECTOR"
><SPAN
CLASS="TYPE"
>GtsVector</SPAN
></GTKDOCLINK
>).</P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15249"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>Kg</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> Gaussian curvature (a gdouble).</P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15254"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>e1</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> first principal curvature direction (direction of largest curvature).</P
></TD
></TR
><TR
><TD
ALIGN="LEFT"
VALIGN="TOP"
><A
NAME="AEN15259"><SPAN
STYLE="white-space: nowrap"
><CODE
CLASS="PARAMETER"
>e2</CODE
> :</SPAN
></TD
><TD
ALIGN="LEFT"
VALIGN="TOP"
><P
> second principal curvature direction.</P
></TD
></TR
></TBODY
></TABLE
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