Algorithm to construct irregular polygon
I have number of line segments (they represent walls in floor scheme) each accompanied with length and adjacent angle. What sequence of steps should my algorithm perform in order to obtain set of vertices for irregular polygon which will correspond to given side lengths and angles?
geometry algorithms polygons
edited Jan 1 at 22:19
David G. Stork
9,87021232
asked Jan 1 at 21:53
Anatoly Strashkevich
184411
add a comment |
I have number of line segments (they represent walls in floor scheme) each accompanied with length and adjacent angle. What sequence of steps should my algorithm perform in order to obtain set of vertices for irregular polygon which will correspond to given side lengths and angles?
geometry algorithms polygons
edited Jan 1 at 22:19
David G. Stork
9,87021232
asked Jan 1 at 21:53
Anatoly Strashkevich
184411
Might you include a picture showing what the adjacent angles are in terms of the sides entering and leaving a vertex? It seems to me that once you know one vertex, you can find the remaining vertices one by one. For convenient, maybe set the first vertex to be $(0,0)$.
– D.B.
Jan 1 at 21:59
Basically i know all internal angles for every corner i just need to turn this thing from plan with lengths and angles in degrees into polygon for further usage without use of image processing i search here and googled on github and npm but found nothing
– Anatoly Strashkevich
Jan 1 at 22:06
I recommend coordinatizing the plane of the floor, and, starting with one corner, using the trigonometry of right triangles to get the coordinates of each corner in turn. You might consider this simple-minded, but it is an algorithm, and it will work.
– Lubin
Jan 2 at 1:21
add a comment |
I have number of line segments (they represent walls in floor scheme) each accompanied with length and adjacent angle. What sequence of steps should my algorithm perform in order to obtain set of vertices for irregular polygon which will correspond to given side lengths and angles?
geometry algorithms polygons
edited Jan 1 at 22:19
David G. Stork
9,87021232
asked Jan 1 at 21:53
Anatoly Strashkevich
184411
I have number of line segments (they represent walls in floor scheme) each accompanied with length and adjacent angle. What sequence of steps should my algorithm perform in order to obtain set of vertices for irregular polygon which will correspond to given side lengths and angles?
geometry algorithms polygons
geometry algorithms polygons
edited Jan 1 at 22:19
David G. Stork
9,87021232
asked Jan 1 at 21:53
Anatoly Strashkevich
184411
edited Jan 1 at 22:19
David G. Stork
9,87021232
asked Jan 1 at 21:53
Anatoly Strashkevich
184411
edited Jan 1 at 22:19
David G. Stork
9,87021232
edited Jan 1 at 22:19
David G. Stork
9,87021232
edited Jan 1 at 22:19
David G. Stork
9,87021232
9,87021232
asked Jan 1 at 21:53
Anatoly Strashkevich
184411
asked Jan 1 at 21:53
Anatoly Strashkevich
184411
asked Jan 1 at 21:53
Anatoly Strashkevich
184411
184411
Might you include a picture showing what the adjacent angles are in terms of the sides entering and leaving a vertex? It seems to me that once you know one vertex, you can find the remaining vertices one by one. For convenient, maybe set the first vertex to be $(0,0)$.
– D.B.
Jan 1 at 21:59
Basically i know all internal angles for every corner i just need to turn this thing from plan with lengths and angles in degrees into polygon for further usage without use of image processing i search here and googled on github and npm but found nothing
– Anatoly Strashkevich
Jan 1 at 22:06
I recommend coordinatizing the plane of the floor, and, starting with one corner, using the trigonometry of right triangles to get the coordinates of each corner in turn. You might consider this simple-minded, but it is an algorithm, and it will work.
– Lubin
Jan 2 at 1:21
add a comment |
Might you include a picture showing what the adjacent angles are in terms of the sides entering and leaving a vertex? It seems to me that once you know one vertex, you can find the remaining vertices one by one. For convenient, maybe set the first vertex to be $(0,0)$.
– D.B.
Jan 1 at 21:59
Basically i know all internal angles for every corner i just need to turn this thing from plan with lengths and angles in degrees into polygon for further usage without use of image processing i search here and googled on github and npm but found nothing
– Anatoly Strashkevich
Jan 1 at 22:06
I recommend coordinatizing the plane of the floor, and, starting with one corner, using the trigonometry of right triangles to get the coordinates of each corner in turn. You might consider this simple-minded, but it is an algorithm, and it will work.
– Lubin
Jan 2 at 1:21
Might you include a picture showing what the adjacent angles are in terms of the sides entering and leaving a vertex? It seems to me that once you know one vertex, you can find the remaining vertices one by one. For convenient, maybe set the first vertex to be $(0,0)$.
– D.B.
Jan 1 at 21:59
Might you include a picture showing what the adjacent angles are in terms of the sides entering and leaving a vertex? It seems to me that once you know one vertex, you can find the remaining vertices one by one. For convenient, maybe set the first vertex to be $(0,0)$.
– D.B.
Jan 1 at 21:59
Basically i know all internal angles for every corner i just need to turn this thing from plan with lengths and angles in degrees into polygon for further usage without use of image processing i search here and googled on github and npm but found nothing
– Anatoly Strashkevich
Jan 1 at 22:06
Basically i know all internal angles for every corner i just need to turn this thing from plan with lengths and angles in degrees into polygon for further usage without use of image processing i search here and googled on github and npm but found nothing
– Anatoly Strashkevich
Jan 1 at 22:06
I recommend coordinatizing the plane of the floor, and, starting with one corner, using the trigonometry of right triangles to get the coordinates of each corner in turn. You might consider this simple-minded, but it is an algorithm, and it will work.
– Lubin
Jan 2 at 1:21
I recommend coordinatizing the plane of the floor, and, starting with one corner, using the trigonometry of right triangles to get the coordinates of each corner in turn. You might consider this simple-minded, but it is an algorithm, and it will work.
– Lubin
Jan 2 at 1:21
add a comment |
1 Answer
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Suppose that the floor plan of your room is a polygon with $n$ sides and vertices $A_1,A_2,dots A_{n}$. The length of segments are:
$$l_1=overline{A_1A_2}, l_2=overline{A_2A_3}, dots l_i=overline{A_iA_{i+1}}, dots l_{n-1}=overline{A_{n-1}A_{n}}, l_n=overline{A_nA_{1}}$$
These lengths are given as well as internal angles of the polygon. Denote angle at point $A_i$ with $alpha_i$. Basically, on input you have a set of values $l_i,alpha_i$ for $i=1,2,dots n$. Your task is to compute coordinates of all vertices.
Suppose that you have already caclulated coordinates $A_i(x_i,y_i)$ and angle $beta_{i-1}$ between segment $A_{i-1}A_i$ and $x$-axis.
Coordinates of point $A_{i+1}$ are given with the following expressions:
$$beta_i=beta_{i-1}+pi-alpha_itag{1}$$
$$x_{i+1}=x_i+l_icosbeta_{i}tag{2}$$
$$y_{i+1}=y_i+l_isinbeta_{i}tag{3}$$
You need a starting point. You are free to choose $A_1$ to be the orgin of your coordinate system:
$$x_1=y_1=0 tag{4}$$
You can orient your $x$-axis along the segment $A_1A_2$ which means that:
$$x_2=l_1, y_2=0, beta_1=0tag{5}$$
With initial conditions set as in (4) and (5) you just need to repeat steps (1), (2) and (3) exactly $n-2$ times to calculate coordinates of the remaining $n-2$ polygon vertices:
$$beta_2=beta_1+pi-alpha_2$$
$$x_3=x_2+l_2cosbeta_{2}$$
$$y_3=y_2+l_2sinbeta_2$$
$$beta_3=beta_2+pi-alpha_3$$
$$x_4=x_3+l_3cosbeta_3$$
$$y_4=y_3+l_3sinbeta_3$$
$$dots$$
answered yesterday
Oldboy
7,1191832
thank you for detailed explanation
– Anatoly Strashkevich
yesterday
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Suppose that the floor plan of your room is a polygon with $n$ sides and vertices $A_1,A_2,dots A_{n}$. The length of segments are:
$$l_1=overline{A_1A_2}, l_2=overline{A_2A_3}, dots l_i=overline{A_iA_{i+1}}, dots l_{n-1}=overline{A_{n-1}A_{n}}, l_n=overline{A_nA_{1}}$$
These lengths are given as well as internal angles of the polygon. Denote angle at point $A_i$ with $alpha_i$. Basically, on input you have a set of values $l_i,alpha_i$ for $i=1,2,dots n$. Your task is to compute coordinates of all vertices.
Suppose that you have already caclulated coordinates $A_i(x_i,y_i)$ and angle $beta_{i-1}$ between segment $A_{i-1}A_i$ and $x$-axis.
Coordinates of point $A_{i+1}$ are given with the following expressions:
$$beta_i=beta_{i-1}+pi-alpha_itag{1}$$
$$x_{i+1}=x_i+l_icosbeta_{i}tag{2}$$
$$y_{i+1}=y_i+l_isinbeta_{i}tag{3}$$
You need a starting point. You are free to choose $A_1$ to be the orgin of your coordinate system:
$$x_1=y_1=0 tag{4}$$
You can orient your $x$-axis along the segment $A_1A_2$ which means that:
$$x_2=l_1, y_2=0, beta_1=0tag{5}$$
With initial conditions set as in (4) and (5) you just need to repeat steps (1), (2) and (3) exactly $n-2$ times to calculate coordinates of the remaining $n-2$ polygon vertices:
$$beta_2=beta_1+pi-alpha_2$$
$$x_3=x_2+l_2cosbeta_{2}$$
$$y_3=y_2+l_2sinbeta_2$$
$$beta_3=beta_2+pi-alpha_3$$
$$x_4=x_3+l_3cosbeta_3$$
$$y_4=y_3+l_3sinbeta_3$$
$$dots$$
answered yesterday
Oldboy
7,1191832
thank you for detailed explanation
– Anatoly Strashkevich
yesterday
add a comment |
Suppose that the floor plan of your room is a polygon with $n$ sides and vertices $A_1,A_2,dots A_{n}$. The length of segments are:
$$l_1=overline{A_1A_2}, l_2=overline{A_2A_3}, dots l_i=overline{A_iA_{i+1}}, dots l_{n-1}=overline{A_{n-1}A_{n}}, l_n=overline{A_nA_{1}}$$
These lengths are given as well as internal angles of the polygon. Denote angle at point $A_i$ with $alpha_i$. Basically, on input you have a set of values $l_i,alpha_i$ for $i=1,2,dots n$. Your task is to compute coordinates of all vertices.
Suppose that you have already caclulated coordinates $A_i(x_i,y_i)$ and angle $beta_{i-1}$ between segment $A_{i-1}A_i$ and $x$-axis.
Coordinates of point $A_{i+1}$ are given with the following expressions:
$$beta_i=beta_{i-1}+pi-alpha_itag{1}$$
$$x_{i+1}=x_i+l_icosbeta_{i}tag{2}$$
$$y_{i+1}=y_i+l_isinbeta_{i}tag{3}$$
You need a starting point. You are free to choose $A_1$ to be the orgin of your coordinate system:
$$x_1=y_1=0 tag{4}$$
You can orient your $x$-axis along the segment $A_1A_2$ which means that:
$$x_2=l_1, y_2=0, beta_1=0tag{5}$$
With initial conditions set as in (4) and (5) you just need to repeat steps (1), (2) and (3) exactly $n-2$ times to calculate coordinates of the remaining $n-2$ polygon vertices:
$$beta_2=beta_1+pi-alpha_2$$
$$x_3=x_2+l_2cosbeta_{2}$$
$$y_3=y_2+l_2sinbeta_2$$
$$beta_3=beta_2+pi-alpha_3$$
$$x_4=x_3+l_3cosbeta_3$$
$$y_4=y_3+l_3sinbeta_3$$
$$dots$$
answered yesterday
Oldboy
7,1191832
thank you for detailed explanation
– Anatoly Strashkevich
yesterday
add a comment |
Suppose that the floor plan of your room is a polygon with $n$ sides and vertices $A_1,A_2,dots A_{n}$. The length of segments are:
$$l_1=overline{A_1A_2}, l_2=overline{A_2A_3}, dots l_i=overline{A_iA_{i+1}}, dots l_{n-1}=overline{A_{n-1}A_{n}}, l_n=overline{A_nA_{1}}$$
These lengths are given as well as internal angles of the polygon. Denote angle at point $A_i$ with $alpha_i$. Basically, on input you have a set of values $l_i,alpha_i$ for $i=1,2,dots n$. Your task is to compute coordinates of all vertices.
Suppose that you have already caclulated coordinates $A_i(x_i,y_i)$ and angle $beta_{i-1}$ between segment $A_{i-1}A_i$ and $x$-axis.
Coordinates of point $A_{i+1}$ are given with the following expressions:
$$beta_i=beta_{i-1}+pi-alpha_itag{1}$$
$$x_{i+1}=x_i+l_icosbeta_{i}tag{2}$$
$$y_{i+1}=y_i+l_isinbeta_{i}tag{3}$$
You need a starting point. You are free to choose $A_1$ to be the orgin of your coordinate system:
$$x_1=y_1=0 tag{4}$$
You can orient your $x$-axis along the segment $A_1A_2$ which means that:
$$x_2=l_1, y_2=0, beta_1=0tag{5}$$
With initial conditions set as in (4) and (5) you just need to repeat steps (1), (2) and (3) exactly $n-2$ times to calculate coordinates of the remaining $n-2$ polygon vertices:
$$beta_2=beta_1+pi-alpha_2$$
$$x_3=x_2+l_2cosbeta_{2}$$
$$y_3=y_2+l_2sinbeta_2$$
$$beta_3=beta_2+pi-alpha_3$$
$$x_4=x_3+l_3cosbeta_3$$
$$y_4=y_3+l_3sinbeta_3$$
$$dots$$
answered yesterday
Oldboy
7,1191832
Suppose that the floor plan of your room is a polygon with $n$ sides and vertices $A_1,A_2,dots A_{n}$. The length of segments are:
$$l_1=overline{A_1A_2}, l_2=overline{A_2A_3}, dots l_i=overline{A_iA_{i+1}}, dots l_{n-1}=overline{A_{n-1}A_{n}}, l_n=overline{A_nA_{1}}$$
These lengths are given as well as internal angles of the polygon. Denote angle at point $A_i$ with $alpha_i$. Basically, on input you have a set of values $l_i,alpha_i$ for $i=1,2,dots n$. Your task is to compute coordinates of all vertices.
Suppose that you have already caclulated coordinates $A_i(x_i,y_i)$ and angle $beta_{i-1}$ between segment $A_{i-1}A_i$ and $x$-axis.
Coordinates of point $A_{i+1}$ are given with the following expressions:
$$beta_i=beta_{i-1}+pi-alpha_itag{1}$$
$$x_{i+1}=x_i+l_icosbeta_{i}tag{2}$$
$$y_{i+1}=y_i+l_isinbeta_{i}tag{3}$$
You need a starting point. You are free to choose $A_1$ to be the orgin of your coordinate system:
$$x_1=y_1=0 tag{4}$$
You can orient your $x$-axis along the segment $A_1A_2$ which means that:
$$x_2=l_1, y_2=0, beta_1=0tag{5}$$
With initial conditions set as in (4) and (5) you just need to repeat steps (1), (2) and (3) exactly $n-2$ times to calculate coordinates of the remaining $n-2$ polygon vertices:
$$beta_2=beta_1+pi-alpha_2$$
$$x_3=x_2+l_2cosbeta_{2}$$
$$y_3=y_2+l_2sinbeta_2$$
$$beta_3=beta_2+pi-alpha_3$$
$$x_4=x_3+l_3cosbeta_3$$
$$y_4=y_3+l_3sinbeta_3$$
$$dots$$
answered yesterday
Oldboy
7,1191832
answered yesterday
Oldboy
7,1191832
answered yesterday
Oldboy
7,1191832
answered yesterday
Oldboy
7,1191832
7,1191832
thank you for detailed explanation
– Anatoly Strashkevich
yesterday
add a comment |
thank you for detailed explanation
– Anatoly Strashkevich
yesterday
thank you for detailed explanation
– Anatoly Strashkevich
yesterday
thank you for detailed explanation
– Anatoly Strashkevich
yesterday
add a comment |
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Might you include a picture showing what the adjacent angles are in terms of the sides entering and leaving a vertex? It seems to me that once you know one vertex, you can find the remaining vertices one by one. For convenient, maybe set the first vertex to be $(0,0)$.
– D.B.
Jan 1 at 21:59
Basically i know all internal angles for every corner i just need to turn this thing from plan with lengths and angles in degrees into polygon for further usage without use of image processing i search here and googled on github and npm but found nothing
– Anatoly Strashkevich
Jan 1 at 22:06
I recommend coordinatizing the plane of the floor, and, starting with one corner, using the trigonometry of right triangles to get the coordinates of each corner in turn. You might consider this simple-minded, but it is an algorithm, and it will work.
– Lubin
Jan 2 at 1:21