Mixing
Proper name for Inverted Cartesian coordinate system?
$begingroup$
In most 2D computer graphic rendering applications (HTML Canvas, Flash, etc...), the coordinate system used is like this:
My question is, what is the mathematical/technical name for this kind of coordinate system? Inverted Cartesian?
coordinate-systems
asked Jan 22 '13 at 5:37
Jake WilsonJake Wilson
1386
$endgroup$
add a comment |
$begingroup$
In most 2D computer graphic rendering applications (HTML Canvas, Flash, etc...), the coordinate system used is like this:
My question is, what is the mathematical/technical name for this kind of coordinate system? Inverted Cartesian?
coordinate-systems
asked Jan 22 '13 at 5:37
Jake WilsonJake Wilson
1386
$endgroup$
$begingroup$
The way these axes are oriented is negative that of the "standard" orientation. I guess you could call this the "left-handed" plane, since the cross product here obeys the left-hand rule.
$endgroup$
– A Blumenthal
Jan 22 '13 at 6:05
$begingroup$
@ABlumenthal What does cross product mean here? There is no $z$ axis.
$endgroup$
– Trevor Wilson
Jan 22 '13 at 6:07
1
$begingroup$
Math can't really tell us what a coordinate system "is", just how to change from one to another. Because you are considering two systems related by a reflection, you could call one of them "reflected Cartesian coordinates" (which one of the two is "reflected" is just a matter of convention.)
$endgroup$
– Trevor Wilson
Jan 22 '13 at 6:10
add a comment |
$begingroup$
In most 2D computer graphic rendering applications (HTML Canvas, Flash, etc...), the coordinate system used is like this:
My question is, what is the mathematical/technical name for this kind of coordinate system? Inverted Cartesian?
coordinate-systems
asked Jan 22 '13 at 5:37
Jake WilsonJake Wilson
1386
$endgroup$
In most 2D computer graphic rendering applications (HTML Canvas, Flash, etc...), the coordinate system used is like this:
My question is, what is the mathematical/technical name for this kind of coordinate system? Inverted Cartesian?
coordinate-systems
coordinate-systems
asked Jan 22 '13 at 5:37
Jake WilsonJake Wilson
1386
asked Jan 22 '13 at 5:37
Jake WilsonJake Wilson
1386
asked Jan 22 '13 at 5:37
Jake WilsonJake Wilson
1386
asked Jan 22 '13 at 5:37
Jake WilsonJake Wilson
1386
asked Jan 22 '13 at 5:37
Jake WilsonJake Wilson
1386
1386
$begingroup$
The way these axes are oriented is negative that of the "standard" orientation. I guess you could call this the "left-handed" plane, since the cross product here obeys the left-hand rule.
$endgroup$
– A Blumenthal
Jan 22 '13 at 6:05
$begingroup$
@ABlumenthal What does cross product mean here? There is no $z$ axis.
$endgroup$
– Trevor Wilson
Jan 22 '13 at 6:07
1
$begingroup$
Math can't really tell us what a coordinate system "is", just how to change from one to another. Because you are considering two systems related by a reflection, you could call one of them "reflected Cartesian coordinates" (which one of the two is "reflected" is just a matter of convention.)
$endgroup$
– Trevor Wilson
Jan 22 '13 at 6:10
add a comment |
$begingroup$
The way these axes are oriented is negative that of the "standard" orientation. I guess you could call this the "left-handed" plane, since the cross product here obeys the left-hand rule.
$endgroup$
– A Blumenthal
Jan 22 '13 at 6:05
$begingroup$
@ABlumenthal What does cross product mean here? There is no $z$ axis.
$endgroup$
– Trevor Wilson
Jan 22 '13 at 6:07
1
$begingroup$
Math can't really tell us what a coordinate system "is", just how to change from one to another. Because you are considering two systems related by a reflection, you could call one of them "reflected Cartesian coordinates" (which one of the two is "reflected" is just a matter of convention.)
$endgroup$
– Trevor Wilson
Jan 22 '13 at 6:10
$begingroup$
The way these axes are oriented is negative that of the "standard" orientation. I guess you could call this the "left-handed" plane, since the cross product here obeys the left-hand rule.
$endgroup$
– A Blumenthal
Jan 22 '13 at 6:05
$begingroup$
The way these axes are oriented is negative that of the "standard" orientation. I guess you could call this the "left-handed" plane, since the cross product here obeys the left-hand rule.
$endgroup$
– A Blumenthal
Jan 22 '13 at 6:05
$begingroup$
@ABlumenthal What does cross product mean here? There is no $z$ axis.
$endgroup$
– Trevor Wilson
Jan 22 '13 at 6:07
$begingroup$
@ABlumenthal What does cross product mean here? There is no $z$ axis.
$endgroup$
– Trevor Wilson
Jan 22 '13 at 6:07
1
1
$begingroup$
Math can't really tell us what a coordinate system "is", just how to change from one to another. Because you are considering two systems related by a reflection, you could call one of them "reflected Cartesian coordinates" (which one of the two is "reflected" is just a matter of convention.)
$endgroup$
– Trevor Wilson
Jan 22 '13 at 6:10
$begingroup$
Math can't really tell us what a coordinate system "is", just how to change from one to another. Because you are considering two systems related by a reflection, you could call one of them "reflected Cartesian coordinates" (which one of the two is "reflected" is just a matter of convention.)
$endgroup$
– Trevor Wilson
Jan 22 '13 at 6:10
add a comment |
1 Answer
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oldest
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$begingroup$
You've tapped into a major incompatability between the standard Math convention taught in Math class, and some CS graphics programming systems (but not all).
I use the term "upside-down y-coordinates" to highlight the problem from a math educator's perspective.
The depth of the problem increases as one delves into more complex spatial problem-solving where vector geometry is advantageous. Here, you want to have strong conventions for representing spatial directions. Standard direction-angles increase CCW, but the designers of "upside-down y-coordinate" graphics toolboxes face a dilemma where they are nudged toward having their direction angles increase CW (so that the trig. functions don't need to be redefined).
Over many years of working in the scientific software area, I have noticed that the "native 2D graphics libraries" are shallow in function when starting off on the wrong foot with inverted ys. This is partly because the early departure from convention cuts off the graphics library developer from advanced, geometric theory.
Khan Academy teaches standard coordinates (y-up) in its Math lectures, and upside-down coordinates (y-down) in its Computer Science graphics lessons (based on JavaScript). That's a confusing approach to be taking.
answered Aug 16 '17 at 1:21
pbierrepbierre
1226
$endgroup$
$begingroup$
Yeah, in most professional, industry-standard 3D software/animation programs, y-up is the norm. But in traditional math classes, z-up is commonly taught. HTML Canvas (as you pointed out using JavaScript) is based on y-down since the origin of the canvas is in the top left corner.
$endgroup$
– Jake Wilson
Aug 16 '17 at 13:26
$begingroup$
I try to separate the discussion of conventions for 2D VS. 3D Cartesian axes. There are many more choices for "standard axes" orientations in 3D. However, if you look at STEM apps in design, CAD, chemistry, applied math, the convention in 3D is for z-up, and x-y in the level plane. x generally points to the right, and y -points back away from the viewer. I've also seen x pointing toward the viewer, and y-pointing to the right, or something in between.
$endgroup$
– pbierre
Aug 16 '17 at 22:18
add a comment |
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$begingroup$
You've tapped into a major incompatability between the standard Math convention taught in Math class, and some CS graphics programming systems (but not all).
I use the term "upside-down y-coordinates" to highlight the problem from a math educator's perspective.
The depth of the problem increases as one delves into more complex spatial problem-solving where vector geometry is advantageous. Here, you want to have strong conventions for representing spatial directions. Standard direction-angles increase CCW, but the designers of "upside-down y-coordinate" graphics toolboxes face a dilemma where they are nudged toward having their direction angles increase CW (so that the trig. functions don't need to be redefined).
Over many years of working in the scientific software area, I have noticed that the "native 2D graphics libraries" are shallow in function when starting off on the wrong foot with inverted ys. This is partly because the early departure from convention cuts off the graphics library developer from advanced, geometric theory.
Khan Academy teaches standard coordinates (y-up) in its Math lectures, and upside-down coordinates (y-down) in its Computer Science graphics lessons (based on JavaScript). That's a confusing approach to be taking.
answered Aug 16 '17 at 1:21
pbierrepbierre
1226
$endgroup$
$begingroup$
Yeah, in most professional, industry-standard 3D software/animation programs, y-up is the norm. But in traditional math classes, z-up is commonly taught. HTML Canvas (as you pointed out using JavaScript) is based on y-down since the origin of the canvas is in the top left corner.
$endgroup$
– Jake Wilson
Aug 16 '17 at 13:26
$begingroup$
I try to separate the discussion of conventions for 2D VS. 3D Cartesian axes. There are many more choices for "standard axes" orientations in 3D. However, if you look at STEM apps in design, CAD, chemistry, applied math, the convention in 3D is for z-up, and x-y in the level plane. x generally points to the right, and y -points back away from the viewer. I've also seen x pointing toward the viewer, and y-pointing to the right, or something in between.
$endgroup$
– pbierre
Aug 16 '17 at 22:18
add a comment |
$begingroup$
You've tapped into a major incompatability between the standard Math convention taught in Math class, and some CS graphics programming systems (but not all).
I use the term "upside-down y-coordinates" to highlight the problem from a math educator's perspective.
The depth of the problem increases as one delves into more complex spatial problem-solving where vector geometry is advantageous. Here, you want to have strong conventions for representing spatial directions. Standard direction-angles increase CCW, but the designers of "upside-down y-coordinate" graphics toolboxes face a dilemma where they are nudged toward having their direction angles increase CW (so that the trig. functions don't need to be redefined).
Over many years of working in the scientific software area, I have noticed that the "native 2D graphics libraries" are shallow in function when starting off on the wrong foot with inverted ys. This is partly because the early departure from convention cuts off the graphics library developer from advanced, geometric theory.
Khan Academy teaches standard coordinates (y-up) in its Math lectures, and upside-down coordinates (y-down) in its Computer Science graphics lessons (based on JavaScript). That's a confusing approach to be taking.
answered Aug 16 '17 at 1:21
pbierrepbierre
1226
$endgroup$
$begingroup$
Yeah, in most professional, industry-standard 3D software/animation programs, y-up is the norm. But in traditional math classes, z-up is commonly taught. HTML Canvas (as you pointed out using JavaScript) is based on y-down since the origin of the canvas is in the top left corner.
$endgroup$
– Jake Wilson
Aug 16 '17 at 13:26
$begingroup$
I try to separate the discussion of conventions for 2D VS. 3D Cartesian axes. There are many more choices for "standard axes" orientations in 3D. However, if you look at STEM apps in design, CAD, chemistry, applied math, the convention in 3D is for z-up, and x-y in the level plane. x generally points to the right, and y -points back away from the viewer. I've also seen x pointing toward the viewer, and y-pointing to the right, or something in between.
$endgroup$
– pbierre
Aug 16 '17 at 22:18
add a comment |
$begingroup$
You've tapped into a major incompatability between the standard Math convention taught in Math class, and some CS graphics programming systems (but not all).
I use the term "upside-down y-coordinates" to highlight the problem from a math educator's perspective.
The depth of the problem increases as one delves into more complex spatial problem-solving where vector geometry is advantageous. Here, you want to have strong conventions for representing spatial directions. Standard direction-angles increase CCW, but the designers of "upside-down y-coordinate" graphics toolboxes face a dilemma where they are nudged toward having their direction angles increase CW (so that the trig. functions don't need to be redefined).
Over many years of working in the scientific software area, I have noticed that the "native 2D graphics libraries" are shallow in function when starting off on the wrong foot with inverted ys. This is partly because the early departure from convention cuts off the graphics library developer from advanced, geometric theory.
Khan Academy teaches standard coordinates (y-up) in its Math lectures, and upside-down coordinates (y-down) in its Computer Science graphics lessons (based on JavaScript). That's a confusing approach to be taking.
answered Aug 16 '17 at 1:21
pbierrepbierre
1226
$endgroup$
You've tapped into a major incompatability between the standard Math convention taught in Math class, and some CS graphics programming systems (but not all).
I use the term "upside-down y-coordinates" to highlight the problem from a math educator's perspective.
The depth of the problem increases as one delves into more complex spatial problem-solving where vector geometry is advantageous. Here, you want to have strong conventions for representing spatial directions. Standard direction-angles increase CCW, but the designers of "upside-down y-coordinate" graphics toolboxes face a dilemma where they are nudged toward having their direction angles increase CW (so that the trig. functions don't need to be redefined).
Over many years of working in the scientific software area, I have noticed that the "native 2D graphics libraries" are shallow in function when starting off on the wrong foot with inverted ys. This is partly because the early departure from convention cuts off the graphics library developer from advanced, geometric theory.
Khan Academy teaches standard coordinates (y-up) in its Math lectures, and upside-down coordinates (y-down) in its Computer Science graphics lessons (based on JavaScript). That's a confusing approach to be taking.
answered Aug 16 '17 at 1:21
pbierrepbierre
1226
answered Aug 16 '17 at 1:21
pbierrepbierre
1226
answered Aug 16 '17 at 1:21
pbierrepbierre
1226
answered Aug 16 '17 at 1:21
pbierrepbierre
1226
1226
$begingroup$
Yeah, in most professional, industry-standard 3D software/animation programs, y-up is the norm. But in traditional math classes, z-up is commonly taught. HTML Canvas (as you pointed out using JavaScript) is based on y-down since the origin of the canvas is in the top left corner.
$endgroup$
– Jake Wilson
Aug 16 '17 at 13:26
$begingroup$
I try to separate the discussion of conventions for 2D VS. 3D Cartesian axes. There are many more choices for "standard axes" orientations in 3D. However, if you look at STEM apps in design, CAD, chemistry, applied math, the convention in 3D is for z-up, and x-y in the level plane. x generally points to the right, and y -points back away from the viewer. I've also seen x pointing toward the viewer, and y-pointing to the right, or something in between.
$endgroup$
– pbierre
Aug 16 '17 at 22:18
add a comment |
$begingroup$
Yeah, in most professional, industry-standard 3D software/animation programs, y-up is the norm. But in traditional math classes, z-up is commonly taught. HTML Canvas (as you pointed out using JavaScript) is based on y-down since the origin of the canvas is in the top left corner.
$endgroup$
– Jake Wilson
Aug 16 '17 at 13:26
$begingroup$
I try to separate the discussion of conventions for 2D VS. 3D Cartesian axes. There are many more choices for "standard axes" orientations in 3D. However, if you look at STEM apps in design, CAD, chemistry, applied math, the convention in 3D is for z-up, and x-y in the level plane. x generally points to the right, and y -points back away from the viewer. I've also seen x pointing toward the viewer, and y-pointing to the right, or something in between.
$endgroup$
– pbierre
Aug 16 '17 at 22:18
$begingroup$
Yeah, in most professional, industry-standard 3D software/animation programs, y-up is the norm. But in traditional math classes, z-up is commonly taught. HTML Canvas (as you pointed out using JavaScript) is based on y-down since the origin of the canvas is in the top left corner.
$endgroup$
– Jake Wilson
Aug 16 '17 at 13:26
$begingroup$
Yeah, in most professional, industry-standard 3D software/animation programs, y-up is the norm. But in traditional math classes, z-up is commonly taught. HTML Canvas (as you pointed out using JavaScript) is based on y-down since the origin of the canvas is in the top left corner.
$endgroup$
– Jake Wilson
Aug 16 '17 at 13:26
$begingroup$
I try to separate the discussion of conventions for 2D VS. 3D Cartesian axes. There are many more choices for "standard axes" orientations in 3D. However, if you look at STEM apps in design, CAD, chemistry, applied math, the convention in 3D is for z-up, and x-y in the level plane. x generally points to the right, and y -points back away from the viewer. I've also seen x pointing toward the viewer, and y-pointing to the right, or something in between.
$endgroup$
– pbierre
Aug 16 '17 at 22:18
$begingroup$
I try to separate the discussion of conventions for 2D VS. 3D Cartesian axes. There are many more choices for "standard axes" orientations in 3D. However, if you look at STEM apps in design, CAD, chemistry, applied math, the convention in 3D is for z-up, and x-y in the level plane. x generally points to the right, and y -points back away from the viewer. I've also seen x pointing toward the viewer, and y-pointing to the right, or something in between.
$endgroup$
– pbierre
Aug 16 '17 at 22:18
add a comment |
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$begingroup$
The way these axes are oriented is negative that of the "standard" orientation. I guess you could call this the "left-handed" plane, since the cross product here obeys the left-hand rule.
$endgroup$
– A Blumenthal
Jan 22 '13 at 6:05
$begingroup$
@ABlumenthal What does cross product mean here? There is no $z$ axis.
$endgroup$
– Trevor Wilson
Jan 22 '13 at 6:07
1
$begingroup$
Math can't really tell us what a coordinate system "is", just how to change from one to another. Because you are considering two systems related by a reflection, you could call one of them "reflected Cartesian coordinates" (which one of the two is "reflected" is just a matter of convention.)
$endgroup$
– Trevor Wilson
Jan 22 '13 at 6:10