monotonicSteffen
Definition
-- @/lua/common/mathlib.lua:1304
-- 2d, monotonic
function monotonicSteffen(y0, y1, y2, y3, x0, x1, x2, x3, x)
local x1x0, x2x1, x3x2 = x1-x0, x2-x1, x3-x2
local delta0, delta1, delta2 = (y1-y0) / (x1x0 + 1e-30), (y2-y1) / (x2x1 + 1e-30), (y3-y2) / (x3x2 + 1e-30)
local m1 = (sign(delta0)+sign(delta1)) * min(abs(delta0),abs(delta1), 0.5*abs((x2x1*delta0 + x1x0*delta1) / (x2-x0 + 1e-30)))
local m2 = (sign(delta1)+sign(delta2)) * min(abs(delta1),abs(delta2), 0.5*abs((x3x2*delta1 + x2x1*delta2) / (x3-x1 + 1e-30)))
local xx1 = x - x1
local xrel = xx1 / max(x2x1, 1e-30)
return y1 + xx1*(m1 + xrel*(delta1 - m1 + (xrel - 1)*(m1 + m2 - 2*delta1)))
end
Callers
@/lua/ge/extensions/editor/camPathEditor.lua
return clamp(
(monotonicSteffen(0, d12, d12 + d23, d12 + d23 + d34, 0, t1, t1 + t2, t1 + t2 + t3, t1 + t) - d12) / d23,
0,
local rot = catmullRomCentripetal(r1, r2, r3, r4, calculateTnorm(sqrt(r1:distance(r2)), sqrt(r2:distance(r3)), sqrt(r3:distance(r4)), t1, t2, t3, camTLocal)):normalized()
local fov = monotonicSteffen(markers[n1].fov or 60, markers[n2].fov or 60, markers[n3].fov or 60, markers[n4].fov or 60, 0, t1, t1 + t2, t1 + t2 + t3, t1 + camTLocal)
@/lua/ge/extensions/editor/scriptAIEditor.lua
local function calculateTnorm(d12, d23, d34, t1, t2, t3, t)
return clamp((monotonicSteffen(0, d12, d12 + d23, d12 + d23 + d34, 0, t1, t1 + t2, t1 + t2 + t3, t1 + t) - d12) / d23, 0, 1)
end
@/lua/ge/extensions/editor/toolUtilities/geom.lua
catmullRomCentripetalFast(p0, p1, p2, p3, t, 0.5, pts[ctr])
pts[ctr].z = monotonicSteffen(z0, z1, z2, z3, 0, 1, 2, 3, t + 1)
ctr = ctr + 1
local tPlus1 = t + 1
pts[ctr].z = monotonicSteffen(z0, z1, z2, z3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for Z, to stop overshooting under the surface.
wds[ctr] = monotonicSteffen(w0, w1, w2, w3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for the width interpolation.
pts[ctr].z = monotonicSteffen(z0, z1, z2, z3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for Z, to stop overshooting under the surface.
wds[ctr] = monotonicSteffen(w0, w1, w2, w3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for the width interpolation.
ctr = ctr + 1
local tPlus1 = t + 1
pts[ctr].z = monotonicSteffen(z0, z1, z2, z3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for Z, to stop overshooting under the surface.
wds[ctr] = monotonicSteffen(w0, w1, w2, w3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for the width interpolation.
pts[ctr].z = monotonicSteffen(z0, z1, z2, z3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for Z, to stop overshooting under the surface.
wds[ctr] = monotonicSteffen(w0, w1, w2, w3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for the width interpolation.
vels[ctr] = monotonicSteffen(v0, v1, v2, v3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for the velocity interpolation.
wds[ctr] = monotonicSteffen(w0, w1, w2, w3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for the width interpolation.
vels[ctr] = monotonicSteffen(v0, v1, v2, v3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for the velocity interpolation.
lims[ctr] = monotonicSteffen(l0, l1, l2, l3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for the velocity limit interpolation.
vels[ctr] = monotonicSteffen(v0, v1, v2, v3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for the velocity interpolation.
lims[ctr] = monotonicSteffen(l0, l1, l2, l3, 0, 1, 2, 3, tPlus1) -- Use a monotonic spline for the velocity limit interpolation.
ctr = ctr + 1
catmullRomCentripetalFast(n0, n1, n2, n3, t, 0.5, normals[ctr])
divWidths[ctr] = monotonicSteffen(w0, w1, w2, w3, 0, 1, 2, 3, t + 1)
ctr = ctr + 1
catmullRomCentripetalFast(n0, n1, n2, n3, t, 0.5, normals[ctr])
divWidths[ctr] = monotonicSteffen(w0, w1, w2, w3, 0, 1, 2, 3, t + 1)
ctr = ctr + 1
catmullRomCentripetalFast(p0, p1, p2, p3, t, 0.5, divPoints[ctr])
divPoints[ctr].z = monotonicSteffen(z0, z1, z2, z3, 0, 1, 2, 3, tPlus1)
catmullRomCentripetalFast(n0, n1, n2, n3, t, 0.5, normals[ctr])
catmullRomCentripetalFast(n0, n1, n2, n3, t, 0.5, normals[ctr])
divWidths[ctr] = monotonicSteffen(w0, w1, w2, w3, 0, 1, 2, 3, tPlus1)
ctr = ctr + 1
catmullRomCentripetalFast(p0, p1, p2, p3, t, 0.5, divPoints[ctr])
divPoints[ctr].z = monotonicSteffen(z0, z1, z2, z3, 0, 1, 2, 3, tPlus1)
divWidths[ctr] = monotonicSteffen(w0, w1, w2, w3, 0, 1, 2, 3, tPlus1)
ctr = ctr + 1
@/lua/ge/extensions/editor/tech/roadArchitect/geometry.lua
local qPlus1 = q + 1
rDisc[ctr] = monotonicSteffen(p1.rot[0], p2.rot[0], p3.rot[0], p4.rot[0], 0, 1, 2, 3, qPlus1)
oDisc[ctr] = monotonicSteffen(p1.offset, p2.offset, p3.offset, p4.offset, 0, 1, 2, 3, qPlus1)
rDisc[ctr] = monotonicSteffen(p1.rot[0], p2.rot[0], p3.rot[0], p4.rot[0], 0, 1, 2, 3, qPlus1)
oDisc[ctr] = monotonicSteffen(p1.offset, p2.offset, p3.offset, p4.offset, 0, 1, 2, 3, qPlus1)
wDisc[ctr], hLDisc[ctr], hRDisc[ctr] = {}, {}, {}
for k, _ in pairs(p1.widths) do
wDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.widths[k][0], p2.widths[k][0], p3.widths[k][0], p4.widths[k][0], 0, 1, 2, 3, qPlus1))
hLDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.heightsL[k][0], p2.heightsL[k][0], p3.heightsL[k][0], p4.heightsL[k][0], 0, 1, 2, 3, qPlus1))
wDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.widths[k][0], p2.widths[k][0], p3.widths[k][0], p4.widths[k][0], 0, 1, 2, 3, qPlus1))
hLDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.heightsL[k][0], p2.heightsL[k][0], p3.heightsL[k][0], p4.heightsL[k][0], 0, 1, 2, 3, qPlus1))
hRDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.heightsR[k][0], p2.heightsR[k][0], p3.heightsR[k][0], p4.heightsR[k][0], 0, 1, 2, 3, qPlus1))
hLDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.heightsL[k][0], p2.heightsL[k][0], p3.heightsL[k][0], p4.heightsL[k][0], 0, 1, 2, 3, qPlus1))
hRDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.heightsR[k][0], p2.heightsR[k][0], p3.heightsR[k][0], p4.heightsR[k][0], 0, 1, 2, 3, qPlus1))
end
local qPlus1 = q + 1
pDisc[ctr].z = monotonicSteffen(p1.p.z, p2.p.z, p3.p.z, p4.p.z, 0, 1, 2, 3, qPlus1)
rDisc[ctr] = monotonicSteffen(p1.rot[0], p2.rot[0], p3.rot[0], p4.rot[0], 0, 1, 2, 3, qPlus1)
pDisc[ctr].z = monotonicSteffen(p1.p.z, p2.p.z, p3.p.z, p4.p.z, 0, 1, 2, 3, qPlus1)
rDisc[ctr] = monotonicSteffen(p1.rot[0], p2.rot[0], p3.rot[0], p4.rot[0], 0, 1, 2, 3, qPlus1)
oDisc[ctr] = monotonicSteffen(p1.offset, p2.offset, p3.offset, p4.offset, 0, 1, 2, 3, qPlus1)
rDisc[ctr] = monotonicSteffen(p1.rot[0], p2.rot[0], p3.rot[0], p4.rot[0], 0, 1, 2, 3, qPlus1)
oDisc[ctr] = monotonicSteffen(p1.offset, p2.offset, p3.offset, p4.offset, 0, 1, 2, 3, qPlus1)
wDisc[ctr], hLDisc[ctr], hRDisc[ctr] = {}, {}, {}
for k, _ in pairs(p1.widths) do
wDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.widths[k][0], p2.widths[k][0], p3.widths[k][0], p4.widths[k][0], 0, 1, 2, 3, qPlus1))
hLDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.heightsL[k][0], p2.heightsL[k][0], p3.heightsL[k][0], p4.heightsL[k][0], 0, 1, 2, 3, qPlus1))
wDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.widths[k][0], p2.widths[k][0], p3.widths[k][0], p4.widths[k][0], 0, 1, 2, 3, qPlus1))
hLDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.heightsL[k][0], p2.heightsL[k][0], p3.heightsL[k][0], p4.heightsL[k][0], 0, 1, 2, 3, qPlus1))
hRDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.heightsR[k][0], p2.heightsR[k][0], p3.heightsR[k][0], p4.heightsR[k][0], 0, 1, 2, 3, qPlus1))
hLDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.heightsL[k][0], p2.heightsL[k][0], p3.heightsL[k][0], p4.heightsL[k][0], 0, 1, 2, 3, qPlus1))
hRDisc[ctr][k] = im.FloatPtr(monotonicSteffen(p1.heightsR[k][0], p2.heightsR[k][0], p3.heightsR[k][0], p4.heightsR[k][0], 0, 1, 2, 3, qPlus1))
end
@/lua/ge/extensions/core/cameraModes/path.lua
local function calculateTnorm(d12, d23, d34, t1, t2, t3, t)
return clamp((monotonicSteffen(0, d12, d12 + d23, d12 + d23 + d34, 0, t1, t1 + t2, t1 + t2 + t3, t1 + t) - d12) / d23, 0, 1)
end
local rot = catmullRomCentripetal(r1, r2, r3, r4, calculateTnorm(sqrt(r1:distance(r2)), sqrt(r2:distance(r3)), sqrt(r3:distance(r4)), t1, t2, t3, camTLocal)):normalized()
local fov = monotonicSteffen(markers[n1].fov or 60, markers[n2].fov or 60, markers[n3].fov or 60, markers[n4].fov or 60, 0, t1, t1 + t2, t1 + t2 + t3, t1 + camTLocal)
if markers[n1].nearClip then
if markers[n1].nearClip then
local nearClip = monotonicSteffen(markers[n1].nearClip or 0.1, markers[n2].nearClip or 0.1, markers[n3].nearClip or 0.1, markers[n4].nearClip or 0.1, 0, t1, t1 + t2, t1 + t2 + t3, t1 + camTLocal)
data.res.nearClip = nearClip