Add delay buffer utilities to engine_util_misc.

PiperOrigin-RevId: 866450284
Change-Id: I86d6dd6a6f7519640f75ca405fb60a12e8619c86
This commit is contained in:
Yuval Tassa
2026-02-06 07:21:49 -08:00
committed by Copybara-Service
parent 60b5b1d59d
commit 84fa527723
3 changed files with 560 additions and 2 deletions
+209
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@@ -910,6 +910,215 @@ size_t mju_decodeBase64(uint8_t* buf, const char* s) {
}
//------------------------------ delay buffers -----------------------------------------------------
// convert logical index (0=oldest, n-1=newest) to physical index
// cursor points to the newest element (logical index n-1)
static inline int delayPhysicalIndex(int cursor, int n, int logical) {
return (cursor + 1 + logical) % n;
}
// find logical index i such that times[i-1] < t <= times[i], using circular binary search
// returns 0 if t <= times[oldest], n if t > times[newest]
// cursor points to the newest element (logical index n-1)
static int delayFindIndex(const mjtNum* times, int n, int cursor, mjtNum t) {
// get oldest and newest timestamps
int oldest_phys = delayPhysicalIndex(cursor, n, 0);
int newest_phys = delayPhysicalIndex(cursor, n, n-1);
mjtNum t_oldest = times[oldest_phys];
mjtNum t_newest = times[newest_phys];
// before or at first element
if (t <= t_oldest) {
return 0;
}
// after last element
if (t > t_newest) {
return n;
}
// circular binary search: find smallest logical i such that times[phys(i)] >= t
int lo = 0;
int hi = n - 1;
while (hi - lo > 1) {
int mid = (lo + hi) / 2;
int mid_phys = delayPhysicalIndex(cursor, n, mid);
if (times[mid_phys] < t) {
lo = mid;
} else {
hi = mid;
}
}
return hi;
}
// initialize delay buffer with given times and values; times must be strictly increasing
// buffer layout: [user(1), cursor(1), times(n), values(n*dim)]
void mju_delayInit(mjtNum* buf, int n, int dim, const mjtNum* times, const mjtNum* values,
mjtNum user) {
// check strict monotonicity of times
for (int i = 0; i < n-1; i++) {
if (times[i+1] - times[i] < mjMINVAL) {
mjERROR("times must be strictly increasing, got times[%d]=%g >= times[%d]=%g",
i, times[i], i+1, times[i+1]);
}
}
// buf layout: [user(1), cursor(1), times(n), values(n*dim)]
buf[0] = user; // user value
buf[1] = (mjtNum)(n-1); // cursor points to newest (logical index n-1 = physical index n-1)
mjtNum* buf_times = buf + 2;
mjtNum* buf_values = buf + 2 + n;
if (times != buf_times) mju_copy(buf_times, times, n);
if (values) mju_copy(buf_values, values, n*dim);
}
// find insertion slot for time t, maintaining sorted order
// if t matches an existing timestamp, returns pointer to that slot
// if a new sample is inserted, the oldest sample is dropped
// returns pointer to value slot where caller should write dim values
mjtNum* mju_delayInsert(mjtNum* buf, int n, int dim, mjtNum t) {
int cursor = (int)buf[1];
mjtNum* times = buf + 2;
mjtNum* values = buf + 2 + n;
// find logical insertion index: times[i-1] < t <= times[i]
int i = delayFindIndex(times, n, cursor, t);
// exact match at logical i: return pointer to existing slot
if (i < n) {
int phys_i = delayPhysicalIndex(cursor, n, i);
if (mju_abs(t - times[phys_i]) < mjMINVAL) {
return values + phys_i*dim;
}
}
// logical i == 0: new sample is older than oldest, replace oldest slot
if (i == 0) {
int oldest_phys = delayPhysicalIndex(cursor, n, 0);
times[oldest_phys] = t;
return values + oldest_phys*dim;
}
// logical i == n: new sample is newer than newest, advance cursor and write
if (i == n) {
cursor = (cursor + 1) % n;
buf[1] = (mjtNum)cursor;
// cursor now points to the new newest slot (which was the old oldest)
times[cursor] = t;
return values + cursor*dim;
}
// 0 < i < n: out-of-order insertion, shift [1, i-1] left (dropping 0), insert at i-1
for (int j = 0; j < i-1; j++) {
int src_phys = delayPhysicalIndex(cursor, n, j+1);
int dst_phys = delayPhysicalIndex(cursor, n, j);
times[dst_phys] = times[src_phys];
mju_copy(values + dst_phys*dim, values + src_phys*dim, dim);
}
int insert_phys = delayPhysicalIndex(cursor, n, i-1);
times[insert_phys] = t;
return values + insert_phys*dim;
}
// read vector value at time t; interp: 0=zero-order-hold, 1=linear, 2=cubic spline
// returns pointer to sample in buffer on exact match or ZOH (res untouched)
// returns NULL and writes interpolated result to res on interpolation
const mjtNum* mju_delayRead(const mjtNum* buf, int n, int dim, mjtNum* res, mjtNum t, int interp) {
int cursor = (int)buf[1];
const mjtNum* times = buf + 2;
const mjtNum* values = buf + 2 + n;
int oldest_phys = delayPhysicalIndex(cursor, n, 0);
int newest_phys = delayPhysicalIndex(cursor, n, n-1);
mjtNum t_oldest = times[oldest_phys];
mjtNum t_newest = times[newest_phys];
// extrapolate before oldest: return pointer to oldest value
if (t <= t_oldest + mjMINVAL) {
return values + oldest_phys*dim;
}
// extrapolate after newest: return pointer to newest value
if (t >= t_newest - mjMINVAL) {
return values + newest_phys*dim;
}
// find bracketing logical index: times[i-1] < t <= times[i]
int i = delayFindIndex(times, n, cursor, t);
int phys_i = delayPhysicalIndex(cursor, n, i);
// check for exact match at i
if (mju_abs(t - times[phys_i]) < mjMINVAL) {
return values + phys_i*dim;
}
// lo = i-1, hi = i (we know i > 0 because t > t_oldest)
int phys_lo = delayPhysicalIndex(cursor, n, i-1);
int phys_hi = phys_i;
// zero-order hold: return pointer to lo (most recent sample <= t)
if (interp == 0) {
return values + phys_lo*dim;
}
mjtNum dt = times[phys_hi] - times[phys_lo];
mjtNum alpha = (t - times[phys_lo]) / dt;
// piecewise linear interpolation
if (interp == 1) {
for (int d = 0; d < dim; d++) {
res[d] = values[phys_lo*dim+d] + alpha * (values[phys_hi*dim+d] - values[phys_lo*dim+d]);
}
}
// cubic spline interpolation
else {
// Hermite basis functions
mjtNum alpha2 = alpha * alpha;
mjtNum alpha3 = alpha2 * alpha;
mjtNum h00 = 2*alpha3 - 3*alpha2 + 1;
mjtNum h10 = alpha3 - 2*alpha2 + alpha;
mjtNum h01 = -2*alpha3 + 3*alpha2;
mjtNum h11 = alpha3 - alpha2;
for (int d = 0; d < dim; d++) {
// finite differenced catmull-rom slopes, 0 at endpoints (constant extrapolation)
mjtNum m_lo = 0;
if (i > 1) {
int phys_lo_prev = delayPhysicalIndex(cursor, n, i-2);
mjtNum dt_lo = times[phys_hi] - times[phys_lo_prev];
m_lo = (values[phys_hi*dim+d] - values[phys_lo_prev*dim+d]) / dt_lo;
}
mjtNum m_hi = 0;
if (i < n - 1) {
int phys_hi_next = delayPhysicalIndex(cursor, n, i+1);
mjtNum dt_hi = times[phys_hi_next] - times[phys_lo];
m_hi = (values[phys_hi_next*dim+d] - values[phys_lo*dim+d]) / dt_hi;
}
res[d] = h00 * values[phys_lo*dim+d] +
h10 * dt * m_lo +
h01 * values[phys_hi*dim+d] +
h11 * dt * m_hi;
}
}
return NULL;
}
//------------------------------ miscellaneous -----------------------------------------------------
// convert contact force to pyramid representation
+26 -2
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@@ -75,7 +75,7 @@ MJAPI mjtNum mju_evalBasis(const mjtNum x[3], int i, int order);
// interpolate a function at x with given interpolation coefficients and order n
MJAPI void mju_interpolate3D(mjtNum res[3], const mjtNum x[3], const mjtNum* coeff, int order);
// ----------------------------- Base64 -----------------------------------------------------------
// ----------------------------- Base64 ------------------------------------------------------------
// encode data as Base64 into buf (including padding and null char)
// returns number of chars written in buf: 4 * [(ndata + 2) / 3] + 1
@@ -89,7 +89,31 @@ MJAPI size_t mju_isValidBase64(const char* s);
// returns number of bytes decoded (upper limit of 3 * (strlen(s) / 4))
MJAPI size_t mju_decodeBase64(uint8_t* buf, const char* s);
//------------------------------ miscellaneous ----------------------------------------------------
//------------------------------ delay buffers -----------------------------------------------------
// buffer layout: [user(1), cursor(1), times(n), values(n*dim)]
// - user: 1 mjtNum reserved for user data (ignored by these functions)
// - cursor: 1 mjtNum for circular buffer index (integer stored as mjtNum)
// - times: n timestamps, contiguous at buf[2..n+1]
// - values: n*dim values, contiguous at buf[n+2..n+2+n*dim-1]
// total buffer size: 2 + n*(1 + dim)
// initialize delay buffer with given times and values; times must be strictly increasing
// values is size n x dim
MJAPI void mju_delayInit(mjtNum* buf, int n, int dim, const mjtNum* times,
const mjtNum* values, mjtNum user);
// find insertion slot for sample at time t, maintaining sorted order
// returns pointer to value slot (size dim) where caller should write
MJAPI mjtNum* mju_delayInsert(mjtNum* buf, int n, int dim, mjtNum t);
// read vector value at time t; interp: 0=zero-order-hold, 1=linear, 2=cubic spline
// returns pointer to sample in buffer on exact match (res untouched)
// returns NULL and writes interpolated result to res otherwise
MJAPI const mjtNum* mju_delayRead(const mjtNum* buf, int n, int dim,
mjtNum* res, mjtNum t, int interp);
//------------------------------ miscellaneous -----------------------------------------------------
// convert contact force to pyramid representation
MJAPI void mju_encodePyramid(mjtNum* pyramid, const mjtNum* force,
+325
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@@ -15,6 +15,7 @@
// Tests for engine/engine_util_solve.c.
#include <array>
#include <vector>
#include <cmath>
#include <cstddef>
#include <cstdint>
@@ -22,6 +23,7 @@
#include <gmock/gmock.h>
#include <gtest/gtest.h>
#include <gtest/gtest-spi.h>
#include <mujoco/mjdata.h>
#include <mujoco/mujoco.h>
#include "src/engine/engine_util_misc.h"
@@ -722,5 +724,328 @@ TEST_F(Base64Test, decodeAndEncode) {
EXPECT_THAT(buffer2.data(), StrEq(s));
}
// --------------------------------- Delay Buffers ----------------------------
using DelayTest = MujocoTest;
// buffer layout: [user(1), cursor(1), times(n), values(n*dim)]
// cursor points to newest element (logical index n-1)
// after init, cursor=n-1, so physical indices equal logical indices
TEST_F(DelayTest, Init) {
constexpr int n = 4;
constexpr int dim = 1;
mjtNum buf[2 + n + n*dim];
std::vector<mjtNum> times = {4, 6, 8, 10};
std::vector<mjtNum> values = {99, 99, 99, 99};
mju_delayInit(buf, n, dim, times.data(), values.data(), 0.0);
// check header
EXPECT_EQ(buf[0], 0.0); // user
EXPECT_EQ(buf[1], static_cast<mjtNum>(n-1)); // cursor = n-1
// timestamps: [4, 6, 8, 10] (t=10 is newest)
// values: [99, 99, 99, 99]
// verify via read function (logical order)
mjtNum res;
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 4.0, 0), 99.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 10.0, 0), 99.0);
}
TEST_F(DelayTest, Init_Vector) {
constexpr int n = 3;
constexpr int dim = 2;
mjtNum buf[2 + n + n*dim];
std::vector<mjtNum> times = {-2, -1, 0};
std::vector<mjtNum> values = {1.0, 2.0, 1.0, 2.0, 1.0, 2.0};
mju_delayInit(buf, n, dim, times.data(), values.data(), 0.0);
EXPECT_EQ(buf[1], static_cast<mjtNum>(n-1)); // cursor = n-1
// verify via read function
mjtNum res[dim];
const mjtNum* ptr = mju_delayRead(buf, n, dim, res, -2.0, 0);
ASSERT_NE(ptr, nullptr);
EXPECT_EQ(ptr[0], 1.0);
EXPECT_EQ(ptr[1], 2.0);
}
TEST_F(DelayTest, Append) {
constexpr int n = 4;
constexpr int dim = 1;
// Initialize buffer properly, then insert
mjtNum buf[2 + 2*n];
buf[0] = 0.0;
buf[1] = n - 1;
// timestamps: [4, 6, 8, 10]
mjtNum times[] = {4, 6, 8, 10};
mju_copy(buf + 2, times, n);
// values: [0, 0, 0, 0]
mju_zero(buf + 2 + n, n);
// overwrite with specific values
*mju_delayInsert(buf, n, dim, 4.0) = 1.0;
*mju_delayInsert(buf, n, dim, 6.0) = 2.0;
*mju_delayInsert(buf, n, dim, 8.0) = 3.0;
*mju_delayInsert(buf, n, dim, 10.0) = 4.0;
// now append at t=12
*mju_delayInsert(buf, n, dim, 12.0) = 99.0;
// verify logical order: [6, 8, 10, 12] -> [2, 3, 4, 99]
mjtNum res;
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 6.0, 0), 2.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 8.0, 0), 3.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 10.0, 0), 4.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 12.0, 0), 99.0);
// oldest should now be t=6
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 4.0, 0), 2.0);
}
TEST_F(DelayTest, Append_Multiple) {
constexpr int n = 3;
constexpr int dim = 1;
mjtNum buf[2 + 2*n];
buf[0] = 0.0;
buf[1] = n - 1;
mjtNum times[] = {-2, -1, 0};
mju_copy(buf + 2, times, n);
mju_zero(buf + 2 + n, n);
for (int i = 1; i <= 4; i++) {
mjtNum i_real = static_cast<mjtNum>(i);
*mju_delayInsert(buf, n, dim, i_real) = i_real;
}
// Final: logical timestamps [2, 3, 4], values [2, 3, 4]
mjtNum res;
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 2.0, 0), 2.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 3.0, 0), 3.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 4.0, 0), 4.0);
}
TEST_F(DelayTest, ReadVector_ExactMatch) {
constexpr int n = 3;
constexpr int dim = 2;
mjtNum buf[2 + n + n*dim];
buf[0] = 0.0;
buf[1] = n - 1;
mjtNum times[] = {0, 1, 2};
mju_copy(buf + 2, times, n);
mju_zero(buf + 2 + n, n*dim);
// set values: t=0->(1,2), t=1->(3,4), t=2->(5,6)
mjtNum* slot0 = mju_delayInsert(buf, n, dim, 0.0);
slot0[0] = 1.0; slot0[1] = 2.0;
mjtNum* slot1 = mju_delayInsert(buf, n, dim, 1.0);
slot1[0] = 3.0; slot1[1] = 4.0;
mjtNum* slot2 = mju_delayInsert(buf, n, dim, 2.0);
slot2[0] = 5.0; slot2[1] = 6.0;
mjtNum res[dim];
const mjtNum* ptr = mju_delayRead(buf, n, dim, res, 1.0, 0);
ASSERT_NE(ptr, nullptr);
EXPECT_EQ(ptr[0], 3.0);
EXPECT_EQ(ptr[1], 4.0);
}
TEST_F(DelayTest, ReadVector_ZOH) {
constexpr int n = 3;
constexpr int dim = 2;
mjtNum buf[2 + n + n*dim];
buf[0] = 0.0;
buf[1] = n - 1;
mjtNum times[] = {0, 1, 2};
mju_copy(buf + 2, times, n);
mju_zero(buf + 2 + n, n*dim);
mjtNum* slot0 = mju_delayInsert(buf, n, dim, 0.0);
slot0[0] = 1.0; slot0[1] = 2.0;
mjtNum* slot1 = mju_delayInsert(buf, n, dim, 1.0);
slot1[0] = 3.0; slot1[1] = 4.0;
mjtNum* slot2 = mju_delayInsert(buf, n, dim, 2.0);
slot2[0] = 5.0; slot2[1] = 6.0;
mjtNum res[dim];
const mjtNum* ptr = mju_delayRead(buf, n, dim, res, 0.5, 0);
ASSERT_NE(ptr, nullptr);
EXPECT_EQ(ptr[0], 1.0);
EXPECT_EQ(ptr[1], 2.0);
}
TEST_F(DelayTest, ReadVector_Linear) {
constexpr int n = 3;
constexpr int dim = 2;
mjtNum buf[2 + n + n*dim];
buf[0] = 0.0;
buf[1] = n - 1;
mjtNum times[] = {0, 1, 2};
mju_copy(buf + 2, times, n);
mju_zero(buf + 2 + n, n*dim);
mjtNum* slot0 = mju_delayInsert(buf, n, dim, 0.0);
slot0[0] = 1.0; slot0[1] = 2.0;
mjtNum* slot1 = mju_delayInsert(buf, n, dim, 1.0);
slot1[0] = 3.0; slot1[1] = 4.0;
mjtNum* slot2 = mju_delayInsert(buf, n, dim, 2.0);
slot2[0] = 5.0; slot2[1] = 6.0;
mjtNum res[dim];
const mjtNum* ptr = mju_delayRead(buf, n, dim, res, 0.5, 1);
EXPECT_EQ(ptr, nullptr);
EXPECT_THAT(res[0], DoubleNear(2.0, 1e-10)); // (1+3)/2
EXPECT_THAT(res[1], DoubleNear(3.0, 1e-10)); // (2+4)/2
}
TEST_F(DelayTest, InsertOutOfOrder) {
constexpr int n = 4;
constexpr int dim = 1;
mjtNum buf[2 + 2*n];
mjtNum res;
auto reset = [&]() {
buf[0] = 0.0;
buf[1] = n - 1;
mjtNum times[] = {4, 6, 8, 10};
mju_copy(buf + 2, times, n);
mju_zero(buf + 2 + n, n);
*mju_delayInsert(buf, n, dim, 4.0) = 1.0;
*mju_delayInsert(buf, n, dim, 6.0) = 2.0;
*mju_delayInsert(buf, n, dim, 8.0) = 3.0;
*mju_delayInsert(buf, n, dim, 10.0) = 4.0;
};
// insert in middle (between t=8 and t=10)
reset();
*mju_delayInsert(buf, n, dim, 9.0) = 99.0;
// logical: [6, 8, 9, 10] -> [2, 3, 99, 4]
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 6.0, 0), 2.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 8.0, 0), 3.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 9.0, 0), 99.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 10.0, 0), 4.0);
// insert near start (between t=4 and t=6)
reset();
*mju_delayInsert(buf, n, dim, 5.0) = 99.0;
// logical: [5, 6, 8, 10] -> [99, 2, 3, 4]
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 5.0, 0), 99.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 6.0, 0), 2.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 8.0, 0), 3.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 10.0, 0), 4.0);
// insert before oldest (t=3 < t=4): replaces oldest
reset();
*mju_delayInsert(buf, n, dim, 3.0) = 99.0;
// logical: [3, 6, 8, 10] -> [99, 2, 3, 4]
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 3.0, 0), 99.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 6.0, 0), 2.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 8.0, 0), 3.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 10.0, 0), 4.0);
}
TEST_F(DelayTest, InsertReplaceOnCollision) {
constexpr int n = 4;
constexpr int dim = 1;
mjtNum buf[2 + 2*n];
mjtNum res;
auto reset = [&]() {
// timestamps: [4, 6, 8, 10], values initialized to 0
buf[0] = 0.0;
buf[1] = n - 1;
mjtNum times[] = {4, 6, 8, 10};
mju_copy(buf + 2, times, n);
mju_zero(buf + 2 + n, n);
*mju_delayInsert(buf, n, dim, 4.0) = 1.0;
*mju_delayInsert(buf, n, dim, 6.0) = 2.0;
*mju_delayInsert(buf, n, dim, 8.0) = 3.0;
*mju_delayInsert(buf, n, dim, 10.0) = 4.0;
};
// collision in middle (t=8)
reset();
*mju_delayInsert(buf, n, dim, 8.0) = 99.0;
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 4.0, 0), 1.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 6.0, 0), 2.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 8.0, 0), 99.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 10.0, 0), 4.0);
// collision at newest (t=10)
reset();
*mju_delayInsert(buf, n, dim, 10.0) = 99.0;
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 4.0, 0), 1.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 6.0, 0), 2.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 8.0, 0), 3.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 10.0, 0), 99.0);
// collision at oldest (t=4)
reset();
*mju_delayInsert(buf, n, dim, 4.0) = 99.0;
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 4.0, 0), 99.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 6.0, 0), 2.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 8.0, 0), 3.0);
EXPECT_EQ(*mju_delayRead(buf, n, dim, &res, 10.0, 0), 4.0);
}
void TriggerDelayInitNonMonotonic() {
mjtNum buf[10];
mjtNum times[4] = {1, 2, 2, 4}; // not strictly increasing
mjtNum values[4] = {0};
mju_delayInit(buf, 4, 1, times, values, 0.0);
}
TEST_F(DelayTest, Init_NonMonotonic) {
EXPECT_FATAL_FAILURE(TriggerDelayInitNonMonotonic(),
"mju_delayInit: times must be strictly increasing");
}
TEST_F(DelayTest, CubicInterpolation) {
int n = 2;
int dim = 2;
mjtNum buf[100]; // 2 + 2 + 2*2 = 8
buf[0] = 0.0;
buf[1] = n - 1;
mjtNum times[] = {-1, 0};
mju_copy(buf + 2, times, n);
mju_zero(buf + 2 + n, n*dim);
// Insert (0, 0, 1) and (1, 1, 0).
// Dim 0: 0 -> 1. Spline: p(x) = 3x^2 - 2x^3
// Dim 1: 1 -> 0. Spline: p(x) = 1 - 3x^2 + 2x^3
mjtNum* slot0 = mju_delayInsert(buf, n, dim, 0.0);
slot0[0] = 0.0; slot0[1] = 1.0;
mjtNum* slot1 = mju_delayInsert(buf, n, dim, 1.0);
slot1[0] = 1.0; slot1[1] = 0.0;
mjtNum res[2];
// Test midpoint x=0.5
// Dim 0: 0.5
// Dim 1: 1 - 0.5 = 0.5
mju_delayRead(buf, n, dim, res, 0.5, 2);
EXPECT_NEAR(res[0], 0.5, 1e-9);
EXPECT_NEAR(res[1], 0.5, 1e-9);
// Test x=0.25
// Dim 0: 3*0.25^2 - 2*0.25^3
// Dim 1: 1 - (3*0.25^2 - 2*0.25^3)
mju_delayRead(buf, n, dim, res, 0.25, 2);
mjtNum expected_0_25 = 3*0.25*0.25 - 2*0.25*0.25*0.25;
EXPECT_NEAR(res[0], expected_0_25, 1e-9);
EXPECT_NEAR(res[1], 1.0 - expected_0_25, 1e-9);
// Test x=0.8
// Dim 0: 3*0.8^2 - 2*0.8^3
// Dim 1: 1 - (3*0.8^2 - 2*0.8^3)
mju_delayRead(buf, n, dim, res, 0.8, 2);
mjtNum expected_0_8 = 3*0.8*0.8 - 2*0.8*0.8*0.8;
EXPECT_NEAR(res[0], expected_0_8, 1e-9);
EXPECT_NEAR(res[1], 1.0 - expected_0_8, 1e-9);
}
} // namespace
} // namespace mujoco