2D Segments

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Functions

Seg2D	seg2d (...)
Seg2D	seg2d_v (...)
real	seg2d_length (...)
real	seg2d_sqlength (...)
V2D	seg2d_eval (...)
real	seg2d_close_param (...)
real	seg2d_point_sqdist (...)
real	seg2d_sqdist (...)

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Segments are fragments of a line between two points p0 and p1 (Figure 1). They are the simplest geometric primitives, after vectors. We define the t parameter as the normalized position within the segment. Values ​​between 0 and 1 will correspond to internal points of the segment, with the limits t=0 (p0) and t=1 (p1). Out of this range we will have the points outside the segment, but within the line that contains it. For example t=2 would be the point after p1 located at a distance equal to the length of the segment.

• Use seg2d_lengthf to get the length of the segment.
• Use seg2d_close_paramf to get the value of the parameter closest to a certain point.
• Use seg2d_evalf to get the point from the parameter.
• Use seg2d_sqdistf to get the distance (squared) between two segments.

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seg2d ()

Create a 2d segment from its components.

Seg2Df
seg2df(const real32_t x0,
       const real32_t y0,
       const real32_t x1,
       const real32_t y1);

Seg2Dd
seg2dd(const real64_t x0,
       const real64_t y0,
       const real64_t x1,
       const real64_t y1);

Seg2D
Seg2D(const real x0,
      const real y0,
      const real x1,
      const real y1);

x0	X coordinate of the first point.
y0	Y coordinate of the first point.
x1	X coordinate of the second point.
y1	Y coordinate of the second point.

Return

The 2d segment.

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seg2d_v ()

Create a 2d segment from two points.

Seg2Df
seg2d_vf(const V2Df *p0,
         const V2Df *p1);

Seg2Dd
seg2d_vd(const V2Dd *p0,
         const V2Dd *p1);

Seg2D
Seg2D::v(const V2D *p0,
         const V2D *p1);

p0	First point.
p1	Second point.

Return

The 2d segment.

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seg2d_length ()

Gets the length of the segment.

real32_t
seg2d_lengthf(const Seg2Df *seg);

real64_t
seg2d_lengthd(const Seg2Dd *seg);

real
Seg2D::length(const Seg2D *seg);

seg

Segment.

Return

Length.

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seg2d_sqlength ()

Gets the square of the segment length.

real32_t
seg2d_sqlengthf(const Seg2Df *seg);

real64_t
seg2d_sqlengthd(const Seg2Dd *seg);

real
Seg2D::sqlength(const Seg2D *seg);

seg

Segment.

Return

Length square.

Remarks

Avoid calculating square roots if we are only interested in comparing measurements.

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seg2d_eval ()

Gets the point in the segment based on the parameter.

V2Df
seg2d_evalf(const Seg2Df *seg,
            const real32_t t);

V2Dd
seg2d_evald(const Seg2Dd *seg,
            const real64_t t);

V2D
Seg2D::eval(const Seg2D *seg,
            const real t);

seg	Segment.
t	Parameter.

Return

Point on the segment (or on the line that contains it).

Remarks

If t=0 it returns p0. If t=1 it returns p1. Values ​​between (0,1) points within the segment. Other values, points on the line that contains the segment.

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seg2d_close_param ()

Gets the parameter of the segment closest to a given point.

real32_t
seg2d_close_paramf(const Seg2Df *seg,
                   const V2Df *pnt);

real64_t
seg2d_close_paramd(const Seg2Dd *seg,
                   const V2Dd *pnt);

real
Seg2D::close_param(const Seg2D *seg,
                   const V2D *pnt);

seg	Segment.
pnt	Point.

Return

Parameter. See seg2d_evalf.

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seg2d_point_sqdist ()

Gets the squared distance from a point to the segment.

real32_t
seg2d_point_sqdistf(const Seg2Df *seg,
                    const V2Df *pnt,
                    real32_t *t);

real64_t
seg2d_point_sqdistd(const Seg2Dd *seg,
                    const V2Dd *pnt,
                    real64_t *t);

real
Seg2D::point_sqdist(const Seg2D *seg,
                    const V2D *pnt,
                    real *t);

seg	Segment.
pnt	Point.
t	Parameter on the line that contains the segment. See seg2d_close_paramf. It can be NULL if we don't need this value.

Return

Distance square.

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seg2d_sqdist ()

Gets the squared distance between two segments.

real32_t
seg2d_sqdistf(const Seg2Df *seg1,
              const Seg2Df *seg2,
              real32_t *t1,
              real32_t *t2);

real64_t
seg2d_sqdistd(const Seg2Dd *seg1,
              const Seg2Dd *seg2,
              real64_t *t1,
              real64_t *t2);

real
Seg2D::sqdist(const Seg2D *seg1,
              const Seg2D *seg2,
              real *t1,
              real *t2);

seg1	First segment.
seg2	Second segment.
t1	Nearest parameter in seg1. It can be NULL if we don't need this value.
t2	Nearest parameter in seg2. It can be NULL if we don't need this value.

Return

Distance square.

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