added function math.line_intersect

docs/index.html

@@ -145,6 +145,12 @@ <h1>Yutils<span>An ASS typeset utilities library</span></h1>
 Calculates length of given vector.
 </div>
 <div class="function">
+x, y = math.line_intersect(x0, y0, x1, y1, x2, y2, x3, y3, strict)<br>
+Calculates intersection point of two lines.<br>
+<span class="function_parameters">x0, y0, x1, y1</span> are both points of line 1, <span class="function_parameters">x2, y2, x3, y3</span> are points of line 2. <span class="function_parameters">strict</span> is a flag, determining the intersection has to be located on the lines.<br>
+<span class="function_return">x, y</span> can be the intersection point. If both lines are parallel, <span class="function_return">x</span> is <b>nil</b>. If <span class="function_parameters">strict</span> is <b>true</b> and there's no intersection on the strict length lines, <span class="function_return">x</span> is <b>inf</b> (1/0).
+</div>
+<div class="function">
 rx, ry, rz = math.ortho(x1, y1, z1, x2, y2, z2)<br>
 Calculates the orthogonal vector to vectors <span class="function_parameters">x1|y1|z1</span> and <span class="function_parameters">x2|y2|z3</span>.
 </div>

src/Yutils.lua

@@ -19,7 +19,7 @@
 	OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 	THE SOFTWARE.
 	-----------------------------------------------------------------------------------------------------------------
-	Version: 4th November 2014, 04:00 (GMT+1)
+	Version: 13th November 2014, 22:20 (GMT+1)
 	
 	Yutils
 		table
@@ -44,6 +44,7 @@
 				transform(x, y, z[, w]) -> number, number, number, number
 			degree(x1, y1, z1, x2, y2, z2) -> number
 			distance(x, y[, z]) -> number
+			line_intersect(x0, y0, x1, y1, x2, y2, x3, y3, strict) -> number, number|nil|inf
 			ortho(x1, y1, z1, x2, y2, z2) -> number, number, number
 			randomsteps(min, max, step) -> number
 			round(x[, dec]) -> number
@@ -960,6 +961,35 @@ Yutils = {
 			-- Calculate length
 			return z and math.sqrt(x*x + y*y + z*z) or math.sqrt(x*x + y*y)
 		end,
+		line_intersect = function(x0, y0, x1, y1, x2, y2, x3, y3, strict)
+			-- Check arguments
+			if type(x0) ~= "number" or type(y0) ~= "number" or type(x1) ~= "number" or type(y1) ~= "number" or
+				type(x2) ~= "number" or type(y2) ~= "number" or type(x3) ~= "number" or type(y3) ~= "number" or
+				strict ~= nil and type(strict) ~= "boolean" then
+				error("two lines and optional strictness flag expected", 2)
+			end
+			-- Get line vectors & check valid lengths
+			local x10, y10, x32, y32 = x0 - x1, y0 - y1, x2 - x3, y2 - y3
+			if x10 == 0 and y10 == 0 or x32 == 0 and y32 == 0 then
+				error("lines mustn't have zero length", 2)
+			end
+			-- Calculate determinant and check for parallel lines
+			local det = x10 * y32 - y10 * x32
+			if det ~= 0 then
+				-- Calculate line intersection (endless line lengths)
+				local pre, post = (x0 * y1 - y0 * x1), (x2 * y3 - y2 * x3)
+				local ix, iy = (pre * x32 - x10 * post) / det, (pre * y32 - y10 * post) / det
+				-- Check for line intersection with given line lengths
+				if strict then
+					local s, t = x10 ~= 0 and (ix - x1) / x10 or (iy - y1) / y10, x32 ~= 0 and (ix - x3) / x32 or (iy - y3) / y32
+					if s < 0 or s > 1 or t < 0 or t > 1 then
+						return 1/0	-- inf
+					end
+				end
+				-- Return intersection point
+				return ix, iy
+			end
+		end,
 		-- Get orthogonal vector of 2 given vectors
 		ortho = function(x1, y1, z1, x2, y2, z2)
 			-- Check arguments

tests/math.lua

@@ -4,6 +4,7 @@ print("Arc curve: ", Yutils.math.arc_curve(100, 0, 0, 0, 95))
 print("Curve point: ", Yutils.math.bezier(0.5, {{0,0},{4,-10},{8,2},{12,0}}))
 print("Distance: ", Yutils.math.distance(10, -5, -3))
 print("Degree: ", Yutils.math.degree(0,-1,0, -0.1,1,0))
+print("Lines intersection: ", Yutils.math.line_intersect(0, 0, 10, 10, 1, 0, 9, 10, true))
 print("Orthogonal: ", Yutils.math.ortho(1,0,0, 0,0,1))
 local mat = Yutils.math.create_matrix().rotate("z", 90).scale(0.5, 2, 2).translate(10, 20, -5)
 print("Transformed point: ", mat.transform(0, 0, 0))