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Find angle and slope of plane passing through 3 points. [closed]
Clash Royale CLAN TAG#URR8PPP
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I have a mesh of non-planar points that create triangular faces. I'm trying to find an equation to determine the angle and slope of a line that will create a sloped plane connecting all three points of each face.
Overall Oblique View
I can create a plane starting at point C but I'm limited to how it can be defined. All I can do is draw a line at an angle (⺠or β), that I can then define the slope (in degrees) or the z value at point d.
Plan/Top View
I'm trying to find the relationship between the three points and the plane that would connect them mathematically. If one line (AB) was parallel to my workplane, the slope would easy but since none of them are, I am trying to get the angle and slope that would define and create the angled plane.
Thanks so much!
-Thom K.
euclidean-geometry plane-geometry slope
asked Aug 6 at 16:05
ThomK
61
closed as unclear what you're asking by Aretino, Lord Shark the Unknown, GNU Supporter, José Carlos Santos, Jyrki Lahtonen Aug 10 at 19:48
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
1
down vote
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I have a mesh of non-planar points that create triangular faces. I'm trying to find an equation to determine the angle and slope of a line that will create a sloped plane connecting all three points of each face.
Overall Oblique View
I can create a plane starting at point C but I'm limited to how it can be defined. All I can do is draw a line at an angle (⺠or β), that I can then define the slope (in degrees) or the z value at point d.
Plan/Top View
I'm trying to find the relationship between the three points and the plane that would connect them mathematically. If one line (AB) was parallel to my workplane, the slope would easy but since none of them are, I am trying to get the angle and slope that would define and create the angled plane.
Thanks so much!
-Thom K.
euclidean-geometry plane-geometry slope
asked Aug 6 at 16:05
ThomK
61
closed as unclear what you're asking by Aretino, Lord Shark the Unknown, GNU Supporter, José Carlos Santos, Jyrki Lahtonen Aug 10 at 19:48
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
It's not clear to me what you're trying to find. You want an expression for what line?
– Tiwa Aina
Aug 6 at 16:50
Thanks for the quick response: I would be looking for the equation for line Cd where I can know angle CAd and the z-coordinate of d.
– ThomK
Aug 6 at 17:00
What is point $D$ determined by? Is it the midpoint of $AB$? The intersection of the angle bisector line through $C$ and $AB$? Or is it dependent on variable $alpha$?
– Tiwa Aina
Aug 6 at 17:11
D is what I'm trying to find: It's the point on AB where the line Cd forms a plane that goes through A, B, C, and d. If A and B had the same Z coordinates, the plane connecting all four points would have angles CdB and CdA at 90. Since they are not, those angles are some other value. The problem I'm having is that I can only create a plane starting at point C and then create the line Cd to define the plane. If I know the slope of Cd (in degrees) and the z-coordinate of d. That would work. Thanks again!
– ThomK
Aug 6 at 17:26
You need two lines to form a plane. You want the plane formed by Cd and what to contain all four points?
– Tiwa Aina
Aug 6 at 17:36
 |Â
show 2 more comments
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I have a mesh of non-planar points that create triangular faces. I'm trying to find an equation to determine the angle and slope of a line that will create a sloped plane connecting all three points of each face.
Overall Oblique View
I can create a plane starting at point C but I'm limited to how it can be defined. All I can do is draw a line at an angle (⺠or β), that I can then define the slope (in degrees) or the z value at point d.
Plan/Top View
I'm trying to find the relationship between the three points and the plane that would connect them mathematically. If one line (AB) was parallel to my workplane, the slope would easy but since none of them are, I am trying to get the angle and slope that would define and create the angled plane.
Thanks so much!
-Thom K.
euclidean-geometry plane-geometry slope
asked Aug 6 at 16:05
ThomK
61
I have a mesh of non-planar points that create triangular faces. I'm trying to find an equation to determine the angle and slope of a line that will create a sloped plane connecting all three points of each face.
Overall Oblique View
I can create a plane starting at point C but I'm limited to how it can be defined. All I can do is draw a line at an angle (⺠or β), that I can then define the slope (in degrees) or the z value at point d.
Plan/Top View
I'm trying to find the relationship between the three points and the plane that would connect them mathematically. If one line (AB) was parallel to my workplane, the slope would easy but since none of them are, I am trying to get the angle and slope that would define and create the angled plane.
Thanks so much!
-Thom K.
euclidean-geometry plane-geometry slope
asked Aug 6 at 16:05
ThomK
61
asked Aug 6 at 16:05
ThomK
61
asked Aug 6 at 16:05
ThomK
61
asked Aug 6 at 16:05
ThomK
61
61
closed as unclear what you're asking by Aretino, Lord Shark the Unknown, GNU Supporter, José Carlos Santos, Jyrki Lahtonen Aug 10 at 19:48
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by Aretino, Lord Shark the Unknown, GNU Supporter, José Carlos Santos, Jyrki Lahtonen Aug 10 at 19:48
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
It's not clear to me what you're trying to find. You want an expression for what line?
– Tiwa Aina
Aug 6 at 16:50
Thanks for the quick response: I would be looking for the equation for line Cd where I can know angle CAd and the z-coordinate of d.
– ThomK
Aug 6 at 17:00
What is point $D$ determined by? Is it the midpoint of $AB$? The intersection of the angle bisector line through $C$ and $AB$? Or is it dependent on variable $alpha$?
– Tiwa Aina
Aug 6 at 17:11
D is what I'm trying to find: It's the point on AB where the line Cd forms a plane that goes through A, B, C, and d. If A and B had the same Z coordinates, the plane connecting all four points would have angles CdB and CdA at 90. Since they are not, those angles are some other value. The problem I'm having is that I can only create a plane starting at point C and then create the line Cd to define the plane. If I know the slope of Cd (in degrees) and the z-coordinate of d. That would work. Thanks again!
– ThomK
Aug 6 at 17:26
You need two lines to form a plane. You want the plane formed by Cd and what to contain all four points?
– Tiwa Aina
Aug 6 at 17:36
 |Â
show 2 more comments
It's not clear to me what you're trying to find. You want an expression for what line?
– Tiwa Aina
Aug 6 at 16:50
Thanks for the quick response: I would be looking for the equation for line Cd where I can know angle CAd and the z-coordinate of d.
– ThomK
Aug 6 at 17:00
What is point $D$ determined by? Is it the midpoint of $AB$? The intersection of the angle bisector line through $C$ and $AB$? Or is it dependent on variable $alpha$?
– Tiwa Aina
Aug 6 at 17:11
D is what I'm trying to find: It's the point on AB where the line Cd forms a plane that goes through A, B, C, and d. If A and B had the same Z coordinates, the plane connecting all four points would have angles CdB and CdA at 90. Since they are not, those angles are some other value. The problem I'm having is that I can only create a plane starting at point C and then create the line Cd to define the plane. If I know the slope of Cd (in degrees) and the z-coordinate of d. That would work. Thanks again!
– ThomK
Aug 6 at 17:26
You need two lines to form a plane. You want the plane formed by Cd and what to contain all four points?
– Tiwa Aina
Aug 6 at 17:36
It's not clear to me what you're trying to find. You want an expression for what line?
– Tiwa Aina
Aug 6 at 16:50
It's not clear to me what you're trying to find. You want an expression for what line?
– Tiwa Aina
Aug 6 at 16:50
Thanks for the quick response: I would be looking for the equation for line Cd where I can know angle CAd and the z-coordinate of d.
– ThomK
Aug 6 at 17:00
Thanks for the quick response: I would be looking for the equation for line Cd where I can know angle CAd and the z-coordinate of d.
– ThomK
Aug 6 at 17:00
What is point $D$ determined by? Is it the midpoint of $AB$? The intersection of the angle bisector line through $C$ and $AB$? Or is it dependent on variable $alpha$?
– Tiwa Aina
Aug 6 at 17:11
What is point $D$ determined by? Is it the midpoint of $AB$? The intersection of the angle bisector line through $C$ and $AB$? Or is it dependent on variable $alpha$?
– Tiwa Aina
Aug 6 at 17:11
D is what I'm trying to find: It's the point on AB where the line Cd forms a plane that goes through A, B, C, and d. If A and B had the same Z coordinates, the plane connecting all four points would have angles CdB and CdA at 90. Since they are not, those angles are some other value. The problem I'm having is that I can only create a plane starting at point C and then create the line Cd to define the plane. If I know the slope of Cd (in degrees) and the z-coordinate of d. That would work. Thanks again!
– ThomK
Aug 6 at 17:26
D is what I'm trying to find: It's the point on AB where the line Cd forms a plane that goes through A, B, C, and d. If A and B had the same Z coordinates, the plane connecting all four points would have angles CdB and CdA at 90. Since they are not, those angles are some other value. The problem I'm having is that I can only create a plane starting at point C and then create the line Cd to define the plane. If I know the slope of Cd (in degrees) and the z-coordinate of d. That would work. Thanks again!
– ThomK
Aug 6 at 17:26
You need two lines to form a plane. You want the plane formed by Cd and what to contain all four points?
– Tiwa Aina
Aug 6 at 17:36
You need two lines to form a plane. You want the plane formed by Cd and what to contain all four points?
– Tiwa Aina
Aug 6 at 17:36
 |Â
show 2 more comments
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It's not clear to me what you're trying to find. You want an expression for what line?
– Tiwa Aina
Aug 6 at 16:50
Thanks for the quick response: I would be looking for the equation for line Cd where I can know angle CAd and the z-coordinate of d.
– ThomK
Aug 6 at 17:00
What is point $D$ determined by? Is it the midpoint of $AB$? The intersection of the angle bisector line through $C$ and $AB$? Or is it dependent on variable $alpha$?
– Tiwa Aina
Aug 6 at 17:11
D is what I'm trying to find: It's the point on AB where the line Cd forms a plane that goes through A, B, C, and d. If A and B had the same Z coordinates, the plane connecting all four points would have angles CdB and CdA at 90. Since they are not, those angles are some other value. The problem I'm having is that I can only create a plane starting at point C and then create the line Cd to define the plane. If I know the slope of Cd (in degrees) and the z-coordinate of d. That would work. Thanks again!
– ThomK
Aug 6 at 17:26
You need two lines to form a plane. You want the plane formed by Cd and what to contain all four points?
– Tiwa Aina
Aug 6 at 17:36