W
werner
I would like to get good instructions to a good and 'stable' method of diagonal tiling.
I suppose there are essentially two kinds of random conditions:
1) On one side (or on two sides, meeting in a hopefully squared angle), one have a determined margin, or border, f.ex. from any earlier tiling what one should now continue. I suppose in that case, one have to start tiling diagonal on that side (or in that corner) and have to stop (f.ex to make a stright, not-diagonal border) at a full multiple of the diagonal size of the tiles at the other side(s) even if then the border at that side will be different than on the starting side
2) No such condition, and perhaps even a not-squared room or area. I suppose one starts in the middle, and stops at both sides on the last possible multiple of the diagonal size of tiles, for make a stright border until the wall, which then will be equal size on all sides (so good as the room is squared)
I suppose, in both cases , one still has the option, to start at a corner, or at the middle point, a) with a joint, or b) with the center of a tile, so that one can adjust the borders to approximately a half diagonal size.
But, how to 'stabilize' the tiling ? The primitive method, would be, to measure and mark a square angle (if not already pre-given by the borders in case 1), and a 45 degree angle in the corner, and then tiling along that 45 degree direction strightly a first base-line, and then starting from that baseline tiling on its two sides. Then one get the corners hopefully in a stright line. This is the theoretical solution, which gives already mess if the angle of the tiles is something else than squared. Or, should one, even in this case, the tiling force to be squared ? But how I track then that the corners always lie in a stright line, specially where I stop to tile (and where should be put potentially a stright border), because adjust and correct everything I can't because meanwhile the paste in the middle of the area already dried.
Another method would be, start at a side border, or at the middle line of the room, and put thereon corners. Either the side corners of the first (uncutted) line at the left or right side of the border/middle line (of each tile, touch with one side corner almost the line), or the upper and lower corner of each tile on the line (if starting from the middle line , for start like this at the edges, one would have to cut the tiles diagonally). In the first case, one would have to stabilize the tiles that they are not rotated and the corners between neighboured tiles are squared, by a second line of tiles at the side fitting in that corners.
A third possibility would be, to mark a squared angle and line to the border or middle line, and start in this angle / corner, putting lines with increasingly 2, 4, 6 (if in the corner meets a joint) or 1, 3, 5 (if in the corner will be an edge) tiles. This also should be self-stabilizing and (best started from the middle of each line, sidewards) most easily adjustable at the sides that the next diagonal edge meets the border / squared-to-it line exactly. Then however one becomes more and more problems to adjust the two sides' last corners exactly in a line, as longer are the lines.
It don't help much to think, that a diagonal tiling (one time made the diagonal baseline) is nothing else than a normal tiling, only seen from a 45 degree angle, and thus, one time one has made the diagonal baseline, one could tile 'normally' stright forward, just stop each line one tile earlier (at each side). Because on normal tiling, one don't have the random conditions - specially that the diagonals also have to lie in stright lines (that's only ocasionally the result, if the tiling is stright)
So I would like to get an explanation from experienced tilers, how to tile best diagonally. As said, the outer corners anyway should be in a stright line, for make a stright (not-diagonal) border to the wall, if not a border at one side already is pre-given.
I suppose there are essentially two kinds of random conditions:
1) On one side (or on two sides, meeting in a hopefully squared angle), one have a determined margin, or border, f.ex. from any earlier tiling what one should now continue. I suppose in that case, one have to start tiling diagonal on that side (or in that corner) and have to stop (f.ex to make a stright, not-diagonal border) at a full multiple of the diagonal size of the tiles at the other side(s) even if then the border at that side will be different than on the starting side
2) No such condition, and perhaps even a not-squared room or area. I suppose one starts in the middle, and stops at both sides on the last possible multiple of the diagonal size of tiles, for make a stright border until the wall, which then will be equal size on all sides (so good as the room is squared)
I suppose, in both cases , one still has the option, to start at a corner, or at the middle point, a) with a joint, or b) with the center of a tile, so that one can adjust the borders to approximately a half diagonal size.
But, how to 'stabilize' the tiling ? The primitive method, would be, to measure and mark a square angle (if not already pre-given by the borders in case 1), and a 45 degree angle in the corner, and then tiling along that 45 degree direction strightly a first base-line, and then starting from that baseline tiling on its two sides. Then one get the corners hopefully in a stright line. This is the theoretical solution, which gives already mess if the angle of the tiles is something else than squared. Or, should one, even in this case, the tiling force to be squared ? But how I track then that the corners always lie in a stright line, specially where I stop to tile (and where should be put potentially a stright border), because adjust and correct everything I can't because meanwhile the paste in the middle of the area already dried.
Another method would be, start at a side border, or at the middle line of the room, and put thereon corners. Either the side corners of the first (uncutted) line at the left or right side of the border/middle line (of each tile, touch with one side corner almost the line), or the upper and lower corner of each tile on the line (if starting from the middle line , for start like this at the edges, one would have to cut the tiles diagonally). In the first case, one would have to stabilize the tiles that they are not rotated and the corners between neighboured tiles are squared, by a second line of tiles at the side fitting in that corners.
A third possibility would be, to mark a squared angle and line to the border or middle line, and start in this angle / corner, putting lines with increasingly 2, 4, 6 (if in the corner meets a joint) or 1, 3, 5 (if in the corner will be an edge) tiles. This also should be self-stabilizing and (best started from the middle of each line, sidewards) most easily adjustable at the sides that the next diagonal edge meets the border / squared-to-it line exactly. Then however one becomes more and more problems to adjust the two sides' last corners exactly in a line, as longer are the lines.
It don't help much to think, that a diagonal tiling (one time made the diagonal baseline) is nothing else than a normal tiling, only seen from a 45 degree angle, and thus, one time one has made the diagonal baseline, one could tile 'normally' stright forward, just stop each line one tile earlier (at each side). Because on normal tiling, one don't have the random conditions - specially that the diagonals also have to lie in stright lines (that's only ocasionally the result, if the tiling is stright)
So I would like to get an explanation from experienced tilers, how to tile best diagonally. As said, the outer corners anyway should be in a stright line, for make a stright (not-diagonal) border to the wall, if not a border at one side already is pre-given.
