Find if a point is within a triangle: Difference between revisions
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(→{{header|Evaldraw}}: add image, fixed tri area which is just halved not sq) |
m (→{{header|Evaldraw}}: dist0 considered inside. add comment about positive quadrant) |
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=={{header|Evaldraw}}== |
=={{header|Evaldraw}}== |
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This solution makes use of the x,y plotting function. It allows us to plot an arbitrary function of x,y and set r,g,b colors before we return. This allows us to test all points in the cartesian space and we can pan and zoom the viewport, or mouse over an x,y position we want to see the computed RGB value for. The isPointInside function here works in similar way to many other solutions here, for the 3 points of a triangle we compute 3 line equations. The line equations when evaluated for a x,y point give the distance from the point to the line. The distance is signed. We can use this to return early from isPointInside. Only if all three lines give a result with the same sign can the point be classified as inside the triangle. We can use this property of sidedness and sign to make the method work for both clockwise and anti-clockwise specification of the triangle vertices. If the triangle is clockwise, then the area function returns a positive value. If the triangle is anti clockwise, then the area function returns a negative value, and we can multiply the sgn checks by -1 so a point can still be considered inside. |
This solution makes use of the x,y plotting function. It allows us to plot an arbitrary function of x,y and set r,g,b colors before we return. This allows us to test all points in the cartesian space and we can pan and zoom the viewport, or mouse over an x,y position we want to see the computed RGB value for. The isPointInside function here works in similar way to many other solutions here, for the 3 points of a triangle we compute 3 line equations. The line equations when evaluated for a x,y point give the distance from the point to the line. The distance is signed. We can use this to return early from isPointInside. Only if all three lines give a result with the same sign can the point be classified as inside the triangle. We can use this property of sidedness and sign to make the method work for both clockwise and anti-clockwise specification of the triangle vertices. If the triangle is clockwise, then the area function returns a positive value. If the triangle is anti clockwise, then the area function returns a negative value, and we can multiply the sgn checks by -1 so a point can still be considered inside. A point with distance 0 is also considered inside. |
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[[File:Evaldraw points in triangle.png|thumb|alt=A triangle with vertices set to red, green and blue with interpolation over surface.|plot mode (x,y,&r,&g,&b) allows for plotting of arbitrary functions of (x,y) and return rgb]] |
[[File:Evaldraw points in triangle.png|thumb|alt=A triangle with vertices set to red, green and blue with interpolation over surface.|plot mode (x,y,&r,&g,&b) allows for plotting of arbitrary functions of (x,y) and return rgb]] |
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swap(d0,d1); |
swap(d0,d1); |
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} |
} |
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r = 255*( d1 / area2); |
r = 255*( d1 / area2); // RGB only within 0-255 range if tri verts in positive cartesian quadrant |
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g = 255*( d2 / area2); |
g = 255*( d2 / area2); |
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b = 255*( d0 / area2); |
b = 255*( d0 / area2); |
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if (d0==0) {r=255; g=0; } |
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if (d1==0) {r=255; g=0; } |
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if (d2==0) {r=255; g=0; } |
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return 1; |
return 1; |
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} |
} |
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