The blending of lines and curves

used for:

eliminating sharp edges and making them safer to

R, which blends with two straight lines meeting at any

m and n are given lines;
R – radius of blending;

1) m' and n' are the lines of the blending
centres of the lines m and n;
2) m' and n' are parallel to respective lines
and equidistant to them of the R-distance;
3) m' and n' intersecting in point O;
O is a centre of blending;
4) Points A and B are the points of blending,
They are determined as a intersection of the
perpendicular passed through O to the
given lines m and n.

Solution:

R, which external blends with the line and circle
m is

m' is the line of the blending centres of
the line m;
m' is parallel to m line and equidistant to
it of the R-distance;
3) To draw the arc with radius R+R1 and
centre in point O1;

Solution:

4) O is a centre of blending – intersection of the arc (R+R1) and m';
5) Points A and B are the points of blending: A – result of intersection of perpendicular through O to m-line; B – intersection of the given circle and line of O and O1 connection.

R, which internal blends with the line and circle
m is

m' is the line of the blending centres of
the line m;
m' is parallel to m line and equidistant to
it of the R-distance;
3) To draw the arc with radius R-R1 and
centre in point O1;

Solution:

4) O is a centre of blending – intersection of the arc (R-R1) and m';
5) Points A2 and B1 are the points of blending: A2 – result of intersection of perpendicular through O to m-line; B1 – intersection of the given circle and line of O and O1 connection.

R, which external blends with two circles
m and n are

To draw two arcs: m' with radius R+R1 and centre in point O1 and n' - with radius R+R2 and centre in point O2;
O is a centre of blending – intersection of the arc m' (R+R1) with arc n' (R+R2);

Solution:

3) Points A and B are the points of blending: A – result of intersection of line OO1 with given circle m; B – result of intersection of line OO2 with given circle n.

R, which internal blends with two circles
m and n are

To draw two arcs: m' with radius R-R1 and centre in point O1 and n' - with radius R-R2 and centre in point O2;
O is a centre of blending – intersection of the arc m' (R-R1) with arc n' (R-R2);

Solution:

3) Points A and B are the points of blending: A – result of intersection of line OO1 with given circle m; B – result of intersection of line OO2 with given circle n.

is given circles with a centre in O2;
R– radius

To connect points O1 and O2;
To find the center of O1O2 sector – point C;

Solution:

3) To draw the arc with radius CO1=CO2 and through centre C.
Point A is a tangency point;
Line O2A is a tangent line to the given circle.

is given circles with a centre in O1 and
R1–

To connect points O1 and O2;
To find the center of O1O2 sector –
point C;

Solution:

3) To draw auxiliary circle through the center of a larger circle O2 with radius R2-R1;
4) To draw the arc with radius CO1=CO2 and through centre C.
5) Point K is a point of two auxiliary circles intersection and it is a point of radius O2B passing which is get to the tangency point B;
6) Tangency point A may be found by the line O1A which is parallel to O2B.
7) Line AB is a tangent line to the given circles.