BorlandTalk.com Borland discussion newsgroups   Archives   FAQ   Search   Memberlist   Usergroups   Register   Profile   Log in to check your private messages   Log in  Finding the 'slope' at a x,z point on a heightmap... Goto page 1, 2  Next          BorlandTalk.com Forum Index -> Delphi Graphics View previous topic :: View next topic   Author Message Paul Nicholls Guest Posted: Thu Jun 10, 2004 2:32 am    Post subject: Finding the 'slope' at a x,z point on a heightmap... Hi all, I am interested in finding out the approximate slope at any x,z point in a Byte filled heightmap... I am at the moment creating each pixel in the heightmap texture array depending on the height range, but I now want to add in that if the slope is too steep for some terrain types then I will use rock for example instead. So I need to find out the slope at any x,z point... Does anyone have a small code snipit that can help me? Thanks in advance, Paul Nicholls (Delphi 5/6 Professional) "The plastic veneer of civilization is easily melted in the heat of the moment" - Paul Nicholls [email]paul-nicholls (AT) hotmail (DOT) com[/email] Replace '-' with '_' to reply Back to top Lord Crc Guest Posted: Thu Jun 10, 2004 3:02 am    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... On Thu, 10 Jun 2004 12:32:35 +1000, "Paul Nicholls" <.> wrote: Quote: So I need to find out the slope at any x,z point... normalX = hmap[x+1, z] - hmap[x-1, z]; normalZ = hmap[x, z+1] - hmap[x, z-1]; simplest is to set normalY = 1 and normalize, and use this normal - Asbjørn Back to top Paul Nicholls Guest Posted: Thu Jun 10, 2004 3:15 am    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... Thanks Asbjorn I'll try this... Cheers, Paul. "Lord Crc" <lordcrc (AT) hotmail (DOT) com> wrote Quote: On Thu, 10 Jun 2004 12:32:35 +1000, "Paul Nicholls" <.> wrote: So I need to find out the slope at any x,z point... normalX = hmap[x+1, z] - hmap[x-1, z]; normalZ = hmap[x, z+1] - hmap[x, z-1]; simplest is to set normalY = 1 and normalize, and use this normal - Asbjørn Back to top Sean Guest Posted: Thu Jun 10, 2004 3:20 am    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... "Paul Nicholls" <.> wrote Quote: Hi all, I am interested in finding out the approximate slope at any x,z point in a Byte filled heightmap... I am at the moment creating each pixel in the heightmap texture array depending on the height range, but I now want to add in that if the slope is too steep for some terrain types then I will use rock for example instead. So I need to find out the slope at any x,z point... For your case: MaxGrad[i,j] := Max ( Abs(y[i,j]-y[i-1,j]) , Abs(y[i,j]-y[i,j-1]) {, Abs(y[i,j]-y[i-1,j-1])/1.41) } ) Back to top Lord Crc Guest Posted: Thu Jun 10, 2004 4:46 am    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... On Thu, 10 Jun 2004 13:15:46 +1000, "Paul Nicholls" <.> wrote: Quote: Thanks Asbjorn Btw, adjust the size of Y to determine how "slopy" you want it. Ie, if it's 1, then since dX or dZ is 1 max too, you wont get any slope angles < 45 deg. So you prob want to decrease it. Here's a small sample of a heightmap "texture" which i made by using the formulate i stated http://lordcrc.no-ip.com/public/hmap.jpg Just a quicky i made after writing this post :) - Asbjørn Back to top Paul Nicholls Guest Posted: Thu Jun 10, 2004 6:08 am    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... erm, I'm actually having trouble using the normal from the calculation you provided so I can blend the two textures... lets say I have the two texture rgb values like so: (r1,g1,b1) = snow (for example) (r2,g2,b2) = rock (for example) t = 0..1 (how to calculate) r := (1-t) * r1 + t * r2; g := (1-t) * g1 + t * g2; b := (1-t) * b1 + t * b2; Given the normal, n, from your calculation and some slope (from vertical) threshold angle, a (0-90), after which the colour interpolates between the snow to the rock depending on the slope, how do I calculate t? So, let say I have a threshold angle of 60 degrees, how can I test it against the normal, and get t? Can you share your code snipit that you used to create the texturemap you posted? "Lord Crc" <lordcrc (AT) hotmail (DOT) com> wrote Quote: On Thu, 10 Jun 2004 13:15:46 +1000, "Paul Nicholls" <.> wrote: Thanks Asbjorn :-) Btw, adjust the size of Y to determine how "slopy" you want it. Ie, if it's 1, then since dX or dZ is 1 max too, you wont get any slope angles < 45 deg. So you prob want to decrease it. Here's a small sample of a heightmap "texture" which i made by using the formulate i stated http://lordcrc.no-ip.com/public/hmap.jpg Just a quicky i made after writing this post :) - Asbjørn Back to top Paul Nicholls Guest Posted: Thu Jun 10, 2004 6:08 am    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... erm, I'm actually having trouble using the normal from the calculation you provided so I can blend the two textures... lets say I have the two texture rgb values like so: (r1,g1,b1) = snow (for example) (r2,g2,b2) = rock (for example) t = 0..1 (how to calculate) r := (1-t) * r1 + t * r2; g := (1-t) * g1 + t * g2; b := (1-t) * b1 + t * b2; Given the normal, n, from your calculation and some slope (from vertical) threshold angle, a (0-90), after which the colour interpolates between the snow to the rock depending on the slope, how do I calculate t? So, let say I have a threshold angle of 60 degrees, how can I test it against the normal, and get t? Can you share your code snipit that you used to create the texturemap you posted? "Lord Crc" <lordcrc (AT) hotmail (DOT) com> wrote Quote: On Thu, 10 Jun 2004 13:15:46 +1000, "Paul Nicholls" <.> wrote: Thanks Asbjorn :-) Btw, adjust the size of Y to determine how "slopy" you want it. Ie, if it's 1, then since dX or dZ is 1 max too, you wont get any slope angles < 45 deg. So you prob want to decrease it. Here's a small sample of a heightmap "texture" which i made by using the formulate i stated http://lordcrc.no-ip.com/public/hmap.jpg Just a quicky i made after writing this post :) - Asbjørn Back to top Nils Haeck Guest Posted: Thu Jun 10, 2004 8:18 pm    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... Hello Paul, I normally visualise Z as the height, based on a field in x and y. If you use that, then: DeltaZx := h(x+1, y) - h(x-1, y); // The difference in Z due to change in x over 2 cells DeltaZy := h(x, y+1) - h(x, y-1); // The difference in Z due to change in y over 2 cells Next you calculate the resulting normal vector using crossproduct: Normal = (2 0 DeltaZx)' x (0 2 DeltaZy) = (-2 * DeltaZx, -2 * DeltaZy, 4), or (-DeltaZx, -DeltaZy, 2) As a result, the slope at (x, y) will be: Slope := sqrt(sqr(DeltaZx) + sqr(DeltaZy)) / 2; So the slope is the biggest amount of change for each one unit of change in the XY plane. It assumes you determine this for * based on the 4 neighbouring cells ABCD see below, so special treatment is neccesary at the edges. B A*C D You could make a small 2D lookup table for most values of DeltaZx and DeltaZy (e.g. in a range of -10 .. 10) and only calculate the slope for values outside of that range. This saves you on the expensive sqrt instruction. Kind regards, Nils Haeck www.simdesign.nl "Paul Nicholls" <.> wrote Quote: Hi all, I am interested in finding out the approximate slope at any x,z point in a Byte filled heightmap... I am at the moment creating each pixel in the heightmap texture array depending on the height range, but I now want to add in that if the slope is too steep for some terrain types then I will use rock for example instead. So I need to find out the slope at any x,z point... Does anyone have a small code snipit that can help me? Thanks in advance, Paul Nicholls (Delphi 5/6 Professional) "The plastic veneer of civilization is easily melted in the heat of the moment" - Paul Nicholls [email]paul-nicholls (AT) hotmail (DOT) com[/email] Replace '-' with '_' to reply Back to top somebody Guest Posted: Thu Jun 10, 2004 11:10 pm    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... "Nils Haeck" <n.haeckno (AT) spamchello (DOT) nl> wrote Quote: Hello Paul, I normally visualise Z as the height, based on a field in x and y. If you use that, then: DeltaZx := h(x+1, y) - h(x-1, y); // The difference in Z due to change in x over 2 cells DeltaZy := h(x, y+1) - h(x, y-1); // The difference in Z due to change in y over 2 cells Technically you should have h(x,y) somewhere above, ie either DeltaZx := h(x+1, y) - h(x, y); or DeltaZx := h(x, y) - h(x-1, y); The problem is, with your definintion, the function h(x,y) = 255*( (x+y) mod 2) would have 0 slope everywhere, which is probably not what one would expect. Quote: Next you calculate the resulting normal vector using crossproduct: Normal = (2 0 DeltaZx)' x (0 2 DeltaZy) = (-2 * DeltaZx, -2 * DeltaZy, 4), or (-DeltaZx, -DeltaZy, 2) As a result, the slope at (x, y) will be: Slope := sqrt(sqr(DeltaZx) + sqr(DeltaZy)) / 2; That's not quite correct either, well, there's no single slope in 3D but a gradient (a vector quantity). So, depending on how "precise" you want to be you can calculate the 4 (or gradients approaching from those directions (for a continuous surface there would only be 2 independent components) and in this case, take the maximum of the absolute values: MaxSlope := Max ( Abs(h(x, y) - h(x-1, y)), Abs(h(x, y) - h(x+1, y)), Abs(h(x, y) - h(x, y-1)), Abs(h(x, y) - h(x, y+1)), 0.71*Abs(h(x, y) - h(x-1, y-1)), 0.71*Abs(h(x, y) - h(x+1, y-1)), 0.71*Abs(h(x, y) - h(x-1, y+1)), 0.71*Abs(h(x, y) - h(x+1, y+1)), ); Back to top Paul Nicholls Guest Posted: Thu Jun 10, 2004 11:14 pm    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... Thanks Nils, I'll give it a go :-) Just one other question, if I have a threshold angle (from vertical), Athreshold, and when the slope is greater than this value (from the vertical), how can I calculate t (0-1) for interpolating between 2 textures (t1 at Athreshold to t2 at 90 degrees)? Can I do this? For example: Athreshold = Cos(60*PI/180); // ignoring the fact I could put in as radians straight off... Normal := Normalise(calculated value at height map point)... D := Dot(Normal,Vector3d(0,1,0)); if(D < Athreshold)then begin t := D / Athreshold; if(t < 0)then t := 0; Rt1 := t1.r; // texture 1 colour Gt1 := t1.g; Bt1 := t1.b; Rt2 := t2.r; // texture 2 colour Gt2 := t2.g; Bt2 := t2.b; R := t * Rt1 + (1-t) * Rt2; G := t * Gt1 + (1-t) * Gt2; B := t * Bt1 + (1-t) * Bt2; end; "Nils Haeck" Quote: Hello Paul, I normally visualise Z as the height, based on a field in x and y. If you use that, then: DeltaZx := h(x+1, y) - h(x-1, y); // The difference in Z due to change in x over 2 cells DeltaZy := h(x, y+1) - h(x, y-1); // The difference in Z due to change in y over 2 cells Next you calculate the resulting normal vector using crossproduct: Normal = (2 0 DeltaZx)' x (0 2 DeltaZy) = (-2 * DeltaZx, -2 * DeltaZy, 4), or (-DeltaZx, -DeltaZy, 2) As a result, the slope at (x, y) will be: Slope := sqrt(sqr(DeltaZx) + sqr(DeltaZy)) / 2; So the slope is the biggest amount of change for each one unit of change in the XY plane. It assumes you determine this for * based on the 4 neighbouring cells ABCD see below, so special treatment is neccesary at the edges. B A*C D You could make a small 2D lookup table for most values of DeltaZx and DeltaZy (e.g. in a range of -10 .. 10) and only calculate the slope for values outside of that range. This saves you on the expensive sqrt instruction. Kind regards, Nils Haeck www.simdesign.nl "Paul Nicholls" <.> wrote Hi all, I am interested in finding out the approximate slope at any x,z point in a Byte filled heightmap... I am at the moment creating each pixel in the heightmap texture array depending on the height range, but I now want to add in that if the slope is too steep for some terrain types then I will use rock for example instead. So I need to find out the slope at any x,z point... Does anyone have a small code snipit that can help me? Thanks in advance, Paul Nicholls (Delphi 5/6 Professional) "The plastic veneer of civilization is easily melted in the heat of the moment" - Paul Nicholls [email]paul-nicholls (AT) hotmail (DOT) com[/email] Replace '-' with '_' to reply Back to top Lord Crc Guest Posted: Thu Jun 10, 2004 11:25 pm    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... On Thu, 10 Jun 2004 16:08:40 +1000, "Paul Nicholls" <.> wrote: Quote: So, let say I have a threshold angle of 60 degrees, how can I test it against the normal, and get t? I used a power curve to blend in the rocks, however i used a elevation threshold for WHEN i started to blend in rocks. You can look at that code to see if does what you want. Quote: Can you share your code snipit that you used to create the texturemap you posted? http://lordcrc.no-ip.com/public/heightmap_slope.zip Its on my home box, so it might die, but i'll make it come back up when i notice :) - Asbjørn Back to top Paul Nicholls Guest Posted: Fri Jun 11, 2004 12:04 am    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... Thanks, I got the code...I'll take a gander :-) Cheers, Paul. "Lord Crc" <lordcrc (AT) hotmail (DOT) com> wrote Quote: On Thu, 10 Jun 2004 16:08:40 +1000, "Paul Nicholls" <.> wrote: So, let say I have a threshold angle of 60 degrees, how can I test it against the normal, and get t? I used a power curve to blend in the rocks, however i used a elevation threshold for WHEN i started to blend in rocks. You can look at that code to see if does what you want. Can you share your code snipit that you used to create the texturemap you posted? http://lordcrc.no-ip.com/public/heightmap_slope.zip Its on my home box, so it might die, but i'll make it come back up when i notice :) - Asbjørn Back to top Nils Haeck Guest Posted: Fri Jun 11, 2004 2:30 pm    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... Quote: h(x,y) = 255*( (x+y) mod 2) would have 0 slope everywhere, which is probably not what one would expect. Sure that's what I would expect. After all, you want the slope for the pixel value itself. If it goes up by 255 at one end and goes down by 255 at the other end, the average of that is 0. You will only get slopes here if you create an image that is twice as big, or shifted by half a pixel. Calculating slopes on such a high-frequency image makes no sense anyway due to aliasing effects. You would have to filter it first and find that in fact the value of all pixels goes to 127.5. Quote: Slope := sqrt(sqr(DeltaZx) + sqr(DeltaZy)) / 2; That's not quite correct either, well, there's no single slope in 3D but a I don't agree at all. It is absolutely correct when looking at the problem in 3D. If you have both slopes in X and Y at 1 pixel height change at one pixel horizontal change, your slope calculation would still yield 1.0 as slope, while in fact if you come from a 45deg angle you would see a slope of sqrt(2)=1.41. And a marble rolling down at that point would not roll along any of the slopes in X and Y but along the 45degree where the slope is maximum. Of course it depends on how far you would want to look around, but above method is generally used for square grids. Nils Back to top Nils Haeck Guest Posted: Fri Jun 11, 2004 2:36 pm    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... Why not simply convert the slope to degrees? That way you'll get a value from 0 to 90 degrees (0 being horizontal, 90 being vertical). The 90 will never be reached in a height map of bytes, I think the theoretical maximum of the slope would be (at the edge) sqrt(sqr(255) * 2) / 2 = (calculate this yourself) So the slope angle would be: Angle = arctan(Slope) - in radians Then you can interpolate like this: t = Arctan(Slope) / (0.5 * pi); R := t * Rt1 + (1-t) * Rt2; G := t * Gt1 + (1-t) * Gt2; B := t * Bt1 + (1-t) * Bt2; Or substitute for 0.5 * pi the value of sqrt(sqr(255) * 2) / 2. Kind regards, Nils "Paul Nicholls" <.> wrote Quote: Thanks Nils, I'll give it a go :-) Just one other question, if I have a threshold angle (from vertical), Athreshold, and when the slope is greater than this value (from the vertical), how can I calculate t (0-1) for interpolating between 2 textures (t1 at Athreshold to t2 at 90 degrees)? Can I do this? For example: Athreshold = Cos(60*PI/180); // ignoring the fact I could put in as radians straight off... Normal := Normalise(calculated value at height map point)... D := Dot(Normal,Vector3d(0,1,0)); if(D < Athreshold)then begin t := D / Athreshold; if(t < 0)then t := 0; Rt1 := t1.r; // texture 1 colour Gt1 := t1.g; Bt1 := t1.b; Rt2 := t2.r; // texture 2 colour Gt2 := t2.g; Bt2 := t2.b; R := t * Rt1 + (1-t) * Rt2; G := t * Gt1 + (1-t) * Gt2; B := t * Bt1 + (1-t) * Bt2; end; "Nils Haeck" news:40c8bf9b (AT) newsgroups (DOT) borland.com... Hello Paul, I normally visualise Z as the height, based on a field in x and y. If you use that, then: DeltaZx := h(x+1, y) - h(x-1, y); // The difference in Z due to change in x over 2 cells DeltaZy := h(x, y+1) - h(x, y-1); // The difference in Z due to change in y over 2 cells Next you calculate the resulting normal vector using crossproduct: Normal = (2 0 DeltaZx)' x (0 2 DeltaZy) = (-2 * DeltaZx, -2 * DeltaZy, 4), or (-DeltaZx, -DeltaZy, 2) As a result, the slope at (x, y) will be: Slope := sqrt(sqr(DeltaZx) + sqr(DeltaZy)) / 2; So the slope is the biggest amount of change for each one unit of change in the XY plane. It assumes you determine this for * based on the 4 neighbouring cells ABCD see below, so special treatment is neccesary at the edges. B A*C D You could make a small 2D lookup table for most values of DeltaZx and DeltaZy (e.g. in a range of -10 .. 10) and only calculate the slope for values outside of that range. This saves you on the expensive sqrt instruction. Kind regards, Nils Haeck www.simdesign.nl "Paul Nicholls" <.> wrote in message news:40c7c906 (AT) newsgroups (DOT) borland.com... Hi all, I am interested in finding out the approximate slope at any x,z point in a Byte filled heightmap... I am at the moment creating each pixel in the heightmap texture array depending on the height range, but I now want to add in that if the slope is too steep for some terrain types then I will use rock for example instead. So I need to find out the slope at any x,z point... Does anyone have a small code snipit that can help me? Thanks in advance, Paul Nicholls (Delphi 5/6 Professional) "The plastic veneer of civilization is easily melted in the heat of the moment" - Paul Nicholls [email]paul-nicholls (AT) hotmail (DOT) com[/email] Replace '-' with '_' to reply Back to top Nils Haeck Guest Posted: Fri Jun 11, 2004 2:40 pm    Post subject: Re: Finding the 'slope' at a x,z point on a heightmap... Correction: Quote: Or substitute for 0.5 * pi the value of sqrt(sqr(255) * 2) / 2. Or substitute for 0.5 * pi the value of arctan(sqrt(sqr(255) * 2) / 2). 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